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
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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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Do Mortgage Subsidies Help or Hurt Borrowers?
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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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Do Mortgage Subsidies Help or Hurt Borrowers?
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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
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Amplifies the response of house prices
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First-time buyers can be hurt by mortgage subsidies
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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
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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
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1 −1 q+t 7 / 24
Applied Welfare Analysis (cont’d) I
I
I
Lenders I
Maximize profits (r − rf − ρ)l
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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 =
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ζD,r 1 dp <0. = p dr εS,p − εD,p
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Incidence of Mortgage Subsidies Graphical Representation
(a) Mortgage Market
(b) Housing Market
p
r
S
p(t) p(0) r
S t
r−t 0
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dp =
E ∂S ∂D ∂p − ∂p
2 1 D(t)
M(t)
D(0)
M(0) dt ∂M ∂t
M
0
Do Mortgage Subsidies Help or Hurt Borrowers?
E = −dt ∂D ∂t
D
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Incidence of Mortgage Subsidies Discussion I
Mortgage subsidy fully distort marginal user cost, but received only on fraction financed with mortgage (LTV): as a non-linear subsidy
I
Financial frictions (ρ > 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) ≈
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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
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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
Do Mortgage Subsidies Help or Hurt Borrowers?
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 +
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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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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
I
Equifax Credit Risk Insight Servicing: first-time buyers if no mortgage account 6 prior to mortgage close, 18.5%
I
Assume house tenure is also Ti years
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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
I
Equifax Credit Risk Insight Servicing: first-time buyers if no mortgage account 6 prior to mortgage close, 18.5%
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))
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(1+ri (ϕ))
−1
(1+ri (ϕ))1/12 (1+ri (ϕ))Ti −1
Do Mortgage Subsidies Help or Hurt Borrowers?
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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
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mortgage rate effect <0
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Effects of Eliminating MID by MSA
Description
Mean
Min
Max
Supply elasticity εS,p,j Mortgage demand semielasticity ζD,r,j Housing value (millions) Mortgage price semielasticity ζp,r,j Price change elimination MID Δpj /pj Incidence (percent of house value) Total dollar value of incidence Efficiency loss (bps of house value) Dollar value efficiency loss (millions)
1.49 -15.4 20,888 -6.85 -6.93 -10.3 -2,145 -4.3 -48.7
0.60 -16.1 226 -9.60 -9.83 -12.0 -39,358 -7.1 -151.0
12.15 -15.1 405,673 -1.18 -1.18 -8.6 -24 -3.0 -0.1
Notes: Price elasticities of supply are from Saiz (2010). Author’s calculations based on McDash Analytics, Equifax Credit Risk Insight Servicing and Saiz (2010).
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Price Effects of Eliminating MID by MSA 0%
-2%
-4%
estimate approximation
-6%
-8%
-10% 0
2
4
6
8
10
12
Price House Supply Elasticity Notes: Author’s calculations based on McDash Analytics and Saiz (2010). David Rappoport (FRB)
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Incidence of Eliminating MID by MSA -4%
Buyers
Owners
-6%
-8%
-10%
-12%
-14% 0
2
4
6
8
10
12
Price House Supply Elasticiy Notes: Author’s calculations based on McDash Analytics, Equifax Credit Risk Insight Servicing and Saiz (2010). David Rappoport (FRB)
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Incidence First-Time Buyers Eliminating MID
Notes: Welfare is measured in percent of house value. Author’s calculations based on McDash Analytics, Equifax Credit Risk Insight Servicing, and Saiz (2010). David Rappoport (FRB)
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Incidence First-Time Buyers Eliminating MID
Notes: Welfare is measured in percent of house value. Author’s calculations based on McDash Analytics, Equifax Credit Risk Insight Servicing, and Saiz (2010). David Rappoport (FRB)
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Conclusions I
Characterize effects of mortgage subsidies using sufficient statistics approach considering response of both mortgage rates and house prices
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Mortgage subsidies generate non-linear effects, can hurt first-time buyers, & EB attenuated by house prices
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Estimated effects are large for households, depend on buyer/owner, & smaller for EB
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Focus on mortgages but insights and techniques suitable to other contexts: student, corporate debt, . . .
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