Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor...
Transcript of Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor...
![Page 1: Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor Income, Taxes, Pensions I Labor income process logy(j,h) = y j +h with h+ = reh +#, #](https://reader033.fdocument.org/reader033/viewer/2022060706/6071e7c2049c343b9b5cd331/html5/thumbnails/1.jpg)
Rental Markets and Wealth Inequalityin the Euro Area
Fabian Kindermann and Sebastian Kohls
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Homeownership and Wealth Inequality
DE AT
FR
NL
LU
IT
FI
BE
GR
PT
SI
ES
.5.6
.7.8
Gin
i o
f N
et
To
tal W
ea
lth
.4 .5 .6 .7 .8 .9Homeownership Rate
β = −0.5253∗∗∗ / R2 = 0.81
![Page 3: Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor Income, Taxes, Pensions I Labor income process logy(j,h) = y j +h with h+ = reh +#, #](https://reader033.fdocument.org/reader033/viewer/2022060706/6071e7c2049c343b9b5cd331/html5/thumbnails/3.jpg)
Central Questions
I What does the data tell us about the origins
of this relationship?
I Can we rationalize this relationship in a model?
I Is wealth inequality a bad thing in this context?
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A Preview: Data
I Many renters ↔ Higher wealth inequality
I Wealth is more unequally distributed among renters
compared to the group of homeowners
I Reason: Many renters hold only small amount of wealth
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A Preview: Model
I Life cycle model with heterogeneous agents
I Households consume and save under income risk
I Can buy houses to eitherI live in them (consumption value)
I rent them out to others (investment value)
I Wedge on the rental market for shelter
I Explain 50% of cross-country variation in wealth inequality
I ”Inefficient” rental markets lead to lower wealth inequality
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A Preview: Mechanism
I When rental markets are inefficient:I Households buy houses earlier in life
I Save up quickly for down-payment
I Leads to less individuals with very low wealth
I When rental markets are efficient:I Renting and owning are close substitutes
I Households have time to wait
I Can finance the house that best suits their needs
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The Data
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Household Finance and Consumption Survey
I About household wealth and consumption (like SCF)
I Coordinated by ECB, carried out by national banks
I 15 Euro Area countries (dropped: Cyprus/Malta/Slovakia)
I Available since spring 2013
I First wave data mostly collected in 2010/11
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Insight 1:
Many Rentersl
High Wealth Inequality
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Measure of Inequality
I Drop top 1% wealth holders from sample
I Generalized Entropy Index
GE(0) = − 1N·
N
∑i=1
log(wi
w
)I Log-deviation from mean
I Puts most weight on inequality at bottom
I GE index easily decomposable
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Homeownership and Wealth Inequality
DE
AT
FRNL
LU
IT
FI
BE
GR
PT
SI
ES
.6.8
11.2
1.4
1.6
GE
(0)
of N
et T
ota
l W
ealth
.4 .5 .6 .7 .8 .9Homeownership Rate
β = −1.7603∗∗∗ / R2 = 0.88
Gini p75/p25 incl. Top 1% B95% Positive Working age
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What it is not!
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Homeownership and Income Inequality
DE
AT FR
NL
LU
IT
FI
BE
GR
PT
SI
ES
.15
.2.2
5.3
.35
GE
(0)
of
La
bo
r In
co
me
.4 .5 .6 .7 .8 .9Homeownership Rate
OECD Data
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Fraction of inherited/gifted houses
DE
AT
NL
LU
IT
BE
GR
PT
SI
ES
0.1
.2.3
.4F
ractio
n H
Hs W
ho
In
he
rite
d H
om
e
.4 .5 .6 .7 .8 .9Homeownership Rate
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Insight 2:
Many Rentersl
Many Households with Low Wealth
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Homeownership and Low Wealth Households
DE
AT
FR
NL
LU
IT
FI
BE
GRPT
SIES
.05
.1.1
5.2
.25
.3.3
5F
rac.
We
alth
Lo
we
r 2
5%
of
Av.
Ea
rnin
gs
.4 .5 .6 .7 .8 .9Homeownership Rate
β = −0.4466∗∗∗ / R2 = 0.78
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Insight 3:
Renters are the Ones
to Hold Little Wealth
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Renters Tend to Hold Little Wealth
0.1
.2.3
.4.5
.6.7
Fra
ctio
n o
f P
op
ula
tio
n
0 .5 1 1.5 2 2.5 3 3.5 4Multiples of Group Average Wealth
Owners Renters
Different Country Types
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Insight 4:
Wealth is More Unequally Distributed
Among Renters Compared to the
Group of Homeowners
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Renters are More Unequal
DE AT
FR
NL
LU
IT
FI
BEGR
PT
SI
ES
DEAT
FR
NL
LUIT
FI
BEGR
PT
SIES
0.5
11
.52
2.5
GE
gc o
f N
et
To
tal W
ea
lth
.4 .5 .6 .7 .8 .9Homeownership Rate
Renters Owners
Decomposition
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Insight 5:
In Countries with High Homeownership Rate,
Young Households Hold more Houses
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Homeownership Rate by Age Groups
0.2
.4.6
.81
Ho
me
ow
ne
rsh
ip R
ate
20 25 30 35 40 45 50 55 60 65Age
Low Medium High
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Summary
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Summary
I Many renters ↔ Higher wealth inequality
I Wealth is more unequally distributed among renters
compared to the group of homeowners
I Reason: Many renters hold only small amount of wealth
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A Quantitative Model
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Baseline Setup
I OLG model in an open economy
I Households consume ”food” and shelter
I Earn stochastic income stream
I Can invest in financial assets and real estate
I Non-convex adjustment costs for real estate
I Part of owned real estate can be rented out
I Wedge τ: renting more expensive compared to owning
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Renter (h = 0)
I State: z = (j, η, a, 0)
I Value function
V(z) = maxc,s,a+,h+
[c1−αsα
]1−σ
1− σ+ βE
[V(z+)|η
]I Budget constraint
c + a+ + pss + phh+ + γ(h+, 0)
= ynet(j, η) + [1 + r(a)]a
I LTV requirement and minimum house size
a+ ≥ −λj+1 phh+ and h+ ∈ {0, [h, ∞]}
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Owner (h ≥ h)
I State: z = (j, η, a, h)
I Value function
V(z) = maxc,s,a+,h+
[c1−αsα
]1−σ
1− σ+ βE
[V(z+)|η
]I Budget constraint
c + a+ + ph(h+ − h) + γ(h+, h) + phδhh
= ynet(j, η) + ps(1− τ)(h− s) + [1 + r(a)]a
I LTV requirement/minimum house size/no renting
a+ ≥ −λj+1 phh+ , h+ ∈ {0, [h, ∞]} and s ≤ h
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Production Sector/Housing Market/Open Economy
I Production of ”food” Cobb-Douglas in capital and labor
I Housing stock fixed H
I Small open economy→ fixed world interest rate rw
I Financial intermediation
r(a) =
{rw − κ
2 if a ≥ 0
rw + κ2 if a < 0.
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Government
I Taxes gross income from labor at T(y)
I Pays pensions p(y(ηjr−1)) to retirees
I Government expenditure
G = T − P.
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Market Clearing
I Shelter Market (ps)∫Z1h=0 · s dΦ =
∫Z1h≥h · (1− τ)(h− s) dΦ
I Housing market (ph) ∫Z
h dΦ = H
I Goods market
Y = C + IK + Ih + G + Ψγ + Ψκ
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Calibration
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Calibration: Households
I Maximum age J = 80
I Retirement at age jr = 63
I No uncertain survival
I Expenditure share α = 0.16 (Eurostat)
I Relative risk aversion σ = 2
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Calibration: Capital Markets and Housing
I Interest rates (ECB)
rw = 0.02 and κ = 0.0191
I LTV requirement λ1 = 0.8 (Andrews, 2011)
I Increases linearly to 0 from age 40 to retirement
I Adjustment costs
γ(h+, h) =
{0 if h+ = h
γ0 + γ1|h+ − h| otherwise
I Set γ0 = 5000e and γ1 = 0.05 (Andrews et al. (2011))
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Calibration: Labor Income, Taxes, Pensions
I Labor income process
log y(j, η) = yj + η with η+ = ρeη + ε , ε ∼ N(0, σ2ε ).
I Use cross-section of HH labor earnings from HFCS
(complemented by LIS data for NL and SI)
I Regress on age fixed effects
I Use residuals to determine variance σ2ε with ρ = 0.95
I Smooth out age profiles by piecewise polynomials
I Tax and pension functions for each country following
Guvenen et al. (2014) using OECD data
Profiles Risk Taxes Pensions
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Calibration to Germany
I Impose zero trade balance
I Apply German tax and pension system
I Normalize house price to ph = 1
I β = 0.9569→ share of low-wealth households ≈ 0.30
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The Thought Experiment
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The Thought Experiment
I Simulate the German economy
I Fix housing stock to German level
I Set country specific incomes and policies
I Calibrate τ for each country to match homeownership rate
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Simulation Results
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Homeownership Rates and Wedges
Country HO rate HO Rate τ
Data Model
Germany 44.2% 44.2% 0.1363Austria 47.7% 47.7% 0.1006France 55.3% 55.3% 0.1936Netherlands 57.1% 57.1% 0.2032Luxembourg 67.1% 67.1% 0.3827Italy 68.7% 68.7% 0.3374Finland 69.2% 69.1% 0.4016Belgium 69.6% 69.7% 0.4685Portugal 71.5% 71.5% 0.3401Greece 72.4% 72.4% 0.4214Slovenia 81.8% 81.8% 0.7894Spain 82.7% 82.7% 0.7048
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Model vs. Data 1:
Many Rentersl
High Wealth Inequality
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Homeownership and Wealth Inequality: Data
0.4 0.5 0.6 0.7 0.8 0.9
Homeownership Rate
0.6
0.8
1
1.2
1.4
1.6
GE
(0)
of
Ne
t T
ota
l W
ea
lth
DE
AT
FRNL
LU
IT
FI
BE
PT
GR
SI
ES
β = −1.7603∗∗∗ / R2 = 0.88
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Homeownership and Wealth Inequality: Model
0.4 0.5 0.6 0.7 0.8 0.9
Homeownership Rate
0.6
0.8
1
1.2
1.4
1.6
GE
(0)
of
Ne
t T
ota
l W
ea
lth
DE
AT
FR
NL
LU
IT
FI
BE
PTGR
SIES
β = −1.2499∗∗∗ / R2 = 0.80
![Page 44: Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor Income, Taxes, Pensions I Labor income process logy(j,h) = y j +h with h+ = reh +#, #](https://reader033.fdocument.org/reader033/viewer/2022060706/6071e7c2049c343b9b5cd331/html5/thumbnails/44.jpg)
Explanatory Power of the Model
I Total Sum of Squares
TSS = ∑c
(GEc
data − GEdata)2
I Residual Sum of Squares
RSS = ∑c(GEc
model − GEcdata)
2
I R-squared
R2 = 1− RSSTSS
![Page 45: Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor Income, Taxes, Pensions I Labor income process logy(j,h) = y j +h with h+ = reh +#, #](https://reader033.fdocument.org/reader033/viewer/2022060706/6071e7c2049c343b9b5cd331/html5/thumbnails/45.jpg)
Explanatory Power of the Model
Model SS Data RSS R2
Total 0.5977 0.1199 79.94%
- only rental wedge τ 0.5977 0.3018 49.52%- only income + policy 0.5977 0.3827 35.97%
![Page 46: Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor Income, Taxes, Pensions I Labor income process logy(j,h) = y j +h with h+ = reh +#, #](https://reader033.fdocument.org/reader033/viewer/2022060706/6071e7c2049c343b9b5cd331/html5/thumbnails/46.jpg)
Explanatory Power of the Model
Model SS Data RSS R2
Total 0.5977 0.1199 79.94%- only rental wedge τ 0.5977 0.3018 49.52%
- only income + policy 0.5977 0.3827 35.97%
![Page 47: Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor Income, Taxes, Pensions I Labor income process logy(j,h) = y j +h with h+ = reh +#, #](https://reader033.fdocument.org/reader033/viewer/2022060706/6071e7c2049c343b9b5cd331/html5/thumbnails/47.jpg)
Explanatory Power of the Model
Model SS Data RSS R2
Total 0.5977 0.1199 79.94%- only rental wedge τ 0.5977 0.3018 49.52%- only income + policy 0.5977 0.3827 35.97%
![Page 48: Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor Income, Taxes, Pensions I Labor income process logy(j,h) = y j +h with h+ = reh +#, #](https://reader033.fdocument.org/reader033/viewer/2022060706/6071e7c2049c343b9b5cd331/html5/thumbnails/48.jpg)
Model vs. Data 2:
Many Rentersl
Many Household with Low Wealth
![Page 49: Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor Income, Taxes, Pensions I Labor income process logy(j,h) = y j +h with h+ = reh +#, #](https://reader033.fdocument.org/reader033/viewer/2022060706/6071e7c2049c343b9b5cd331/html5/thumbnails/49.jpg)
Households with Low Wealth: Data
0.4 0.5 0.6 0.7 0.8 0.9
Homeownership Rate
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Fra
c. W
ealth L
ow
er
25%
of A
v. E
arn
ings
DE
AT
FR
NL
LU
IT
FI
BE
PTGR
SIES
β = −0.4466∗∗∗ / R2 = 0.78
![Page 50: Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor Income, Taxes, Pensions I Labor income process logy(j,h) = y j +h with h+ = reh +#, #](https://reader033.fdocument.org/reader033/viewer/2022060706/6071e7c2049c343b9b5cd331/html5/thumbnails/50.jpg)
Households with Low Wealth: Model
0.4 0.5 0.6 0.7 0.8 0.9
Homeownership Rate
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Fra
c. W
ealth L
ow
er
25%
of A
v. E
arn
ings
DE
AT
FR
NL
LU
IT
FIBE
PTGR
SI
ES
β = −0.3473∗∗∗ / R2 = 0.79
![Page 51: Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor Income, Taxes, Pensions I Labor income process logy(j,h) = y j +h with h+ = reh +#, #](https://reader033.fdocument.org/reader033/viewer/2022060706/6071e7c2049c343b9b5cd331/html5/thumbnails/51.jpg)
Model vs. Data 3:
Wealth is More Unequally Distributed
Among Renters Compared to the
Group of Homeowners
![Page 52: Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor Income, Taxes, Pensions I Labor income process logy(j,h) = y j +h with h+ = reh +#, #](https://reader033.fdocument.org/reader033/viewer/2022060706/6071e7c2049c343b9b5cd331/html5/thumbnails/52.jpg)
Renters are More Unequal: Data
0.4 0.5 0.6 0.7 0.8 0.9
Homeownership Rate
0
0.5
1
1.5
2
2.5G
E(0
) o
f N
et
To
tal W
ea
lth
DE
DE
AT
AT
FR
FR
NL
NL
LU
LU
IT
IT
FI
FI
BE
BE
PT
PT
GR
GR
SI
SI
ES
ES
Renters
Owners
![Page 53: Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor Income, Taxes, Pensions I Labor income process logy(j,h) = y j +h with h+ = reh +#, #](https://reader033.fdocument.org/reader033/viewer/2022060706/6071e7c2049c343b9b5cd331/html5/thumbnails/53.jpg)
Renters are More Unequal: Model
0.4 0.5 0.6 0.7 0.8 0.9
Homeownership Rate
0
0.5
1
1.5
2
2.5G
E(0
) o
f N
et
To
tal W
ea
lth
DE
DE
AT
AT
FR
FR
NL
NL
LU
LU
IT
IT
FI
FI
BE
BE
PT
PT
GR
GR
SI
SI
ES
ES
Renters
Owners
![Page 54: Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor Income, Taxes, Pensions I Labor income process logy(j,h) = y j +h with h+ = reh +#, #](https://reader033.fdocument.org/reader033/viewer/2022060706/6071e7c2049c343b9b5cd331/html5/thumbnails/54.jpg)
Model vs. Data 4:
In Countries with High Homeownership Rate,
Young Households Hold more Houses
![Page 55: Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor Income, Taxes, Pensions I Labor income process logy(j,h) = y j +h with h+ = reh +#, #](https://reader033.fdocument.org/reader033/viewer/2022060706/6071e7c2049c343b9b5cd331/html5/thumbnails/55.jpg)
Homeownership Rate by Age Groups: Data
20 25 30 35 40 45 50 55 60 65
Age
0
0.2
0.4
0.6
0.8
1
Ho
me
ow
ne
rsh
ip R
ate
Low Medium High
![Page 56: Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor Income, Taxes, Pensions I Labor income process logy(j,h) = y j +h with h+ = reh +#, #](https://reader033.fdocument.org/reader033/viewer/2022060706/6071e7c2049c343b9b5cd331/html5/thumbnails/56.jpg)
Homeownership Rate by Age Groups: Model
20 25 30 35 40 45 50 55 60 65
Age
0
0.2
0.4
0.6
0.8
1
Ho
me
ow
ne
rsh
ip R
ate
Low Medium High
![Page 57: Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor Income, Taxes, Pensions I Labor income process logy(j,h) = y j +h with h+ = reh +#, #](https://reader033.fdocument.org/reader033/viewer/2022060706/6071e7c2049c343b9b5cd331/html5/thumbnails/57.jpg)
The Underlying Mechanism
![Page 58: Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor Income, Taxes, Pensions I Labor income process logy(j,h) = y j +h with h+ = reh +#, #](https://reader033.fdocument.org/reader033/viewer/2022060706/6071e7c2049c343b9b5cd331/html5/thumbnails/58.jpg)
For Illustration Purposes
I Create a hybrid country out of the 12 sample countries
I Average income profiles and variances
I Average tax and pension policy
I Only vary τ across the countries.
![Page 59: Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor Income, Taxes, Pensions I Labor income process logy(j,h) = y j +h with h+ = reh +#, #](https://reader033.fdocument.org/reader033/viewer/2022060706/6071e7c2049c343b9b5cd331/html5/thumbnails/59.jpg)
Homeownership Rates by Age in the Model
20 30 40 50 60 70 80
Age j
0
0.2
0.4
0.6
0.8
1
Hom
eow
ners
hip
Rate
Low s (Germany) Medium
s (Italy) High
s (Spain)
LTV Constraint
![Page 60: Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor Income, Taxes, Pensions I Labor income process logy(j,h) = y j +h with h+ = reh +#, #](https://reader033.fdocument.org/reader033/viewer/2022060706/6071e7c2049c343b9b5cd331/html5/thumbnails/60.jpg)
Shelter Supply
20 30 40 50 60 70 80
Age j
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2S
helter
Supply
h-s
(R
eal U
nits)
Low s (Germany) Medium
s (Italy) High
s (Spain)
![Page 61: Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor Income, Taxes, Pensions I Labor income process logy(j,h) = y j +h with h+ = reh +#, #](https://reader033.fdocument.org/reader033/viewer/2022060706/6071e7c2049c343b9b5cd331/html5/thumbnails/61.jpg)
Real Estate Investment
20 30 40 50 60 70 80
Age j
0
0.5
1
1.5
2
2.5
3
3.5R
eal E
sta
te p
hh
Low s (Germany) Medium
s (Italy) High
s (Spain)
When Young
![Page 62: Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor Income, Taxes, Pensions I Labor income process logy(j,h) = y j +h with h+ = reh +#, #](https://reader033.fdocument.org/reader033/viewer/2022060706/6071e7c2049c343b9b5cd331/html5/thumbnails/62.jpg)
Financial Assets
20 30 40 50 60 70 80
Age j
-1
0
1
2
3
4
5
Fin
ancia
l A
ssets
a (
Valu
e)
Low s (Germany) Medium
s (Italy) High
s (Spain)
When Young
![Page 63: Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor Income, Taxes, Pensions I Labor income process logy(j,h) = y j +h with h+ = reh +#, #](https://reader033.fdocument.org/reader033/viewer/2022060706/6071e7c2049c343b9b5cd331/html5/thumbnails/63.jpg)
Net Wealth
20 30 40 50 60 70 80
Age j
0
1
2
3
4
5
6
7
8
Net W
ealth (
Valu
e)
Low s (Germany) Medium
s (Italy) High
s (Spain)
When Young
![Page 64: Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor Income, Taxes, Pensions I Labor income process logy(j,h) = y j +h with h+ = reh +#, #](https://reader033.fdocument.org/reader033/viewer/2022060706/6071e7c2049c343b9b5cd331/html5/thumbnails/64.jpg)
Consumption
20 30 40 50 60 70 80
Age j
0
0.1
0.2
0.3
0.4
0.5
0.6
Consum
ption E
xpenditure
c
Low s (Germany) Medium
s (Italy) High
s (Spain)
When Young
![Page 65: Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor Income, Taxes, Pensions I Labor income process logy(j,h) = y j +h with h+ = reh +#, #](https://reader033.fdocument.org/reader033/viewer/2022060706/6071e7c2049c343b9b5cd331/html5/thumbnails/65.jpg)
Shelter
20 30 40 50 60 70 80
Age j
0
0.5
1
1.5
2
2.5
Shelter
s (
Real U
nits)
Low s (Germany) Medium
s (Italy) High
s (Spain)
When Young
![Page 66: Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor Income, Taxes, Pensions I Labor income process logy(j,h) = y j +h with h+ = reh +#, #](https://reader033.fdocument.org/reader033/viewer/2022060706/6071e7c2049c343b9b5cd331/html5/thumbnails/66.jpg)
Some Normative Statement
![Page 67: Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor Income, Taxes, Pensions I Labor income process logy(j,h) = y j +h with h+ = reh +#, #](https://reader033.fdocument.org/reader033/viewer/2022060706/6071e7c2049c343b9b5cd331/html5/thumbnails/67.jpg)
Consumption Equivalent Variation
0.4 0.5 0.6 0.7 0.8 0.9
Homeownership Rate
-10
-8
-6
-4
-2
0
2C
EV
over
livin
g in G
erm
any (
in %
)
DEAT
FRNL
LU
IT
FI
BE
PT
GR
SI
ES
![Page 68: Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor Income, Taxes, Pensions I Labor income process logy(j,h) = y j +h with h+ = reh +#, #](https://reader033.fdocument.org/reader033/viewer/2022060706/6071e7c2049c343b9b5cd331/html5/thumbnails/68.jpg)
Conclusion
![Page 69: Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor Income, Taxes, Pensions I Labor income process logy(j,h) = y j +h with h+ = reh +#, #](https://reader033.fdocument.org/reader033/viewer/2022060706/6071e7c2049c343b9b5cd331/html5/thumbnails/69.jpg)
Conclusion
I Wedge on the rental market can explain the negativecorrelation between wealth inequality and thehomeownership rate across countries
I Our model suggests that countries with very highhomeownership rates could benefit from policies aimed atmaking rental markets work better
I High wealth inequality doesn’t necessarily mean lowerwelfare
![Page 70: Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor Income, Taxes, Pensions I Labor income process logy(j,h) = y j +h with h+ = reh +#, #](https://reader033.fdocument.org/reader033/viewer/2022060706/6071e7c2049c343b9b5cd331/html5/thumbnails/70.jpg)
Gini Index
DE AT
FR
NL
LU
IT
FI
BE
GR
PT
SI
ES
.5.6
.7.8
Gin
i o
f N
et
To
tal W
ea
lth
.4 .5 .6 .7 .8 .9Homeownership Rate
β = −0.5253∗∗∗ / R2 = 0.81 back
![Page 71: Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor Income, Taxes, Pensions I Labor income process logy(j,h) = y j +h with h+ = reh +#, #](https://reader033.fdocument.org/reader033/viewer/2022060706/6071e7c2049c343b9b5cd331/html5/thumbnails/71.jpg)
p75/p25 Ratio
DE
AT
FR
NL
LU
IT
FI
BE
GRPT
SIES
05
10
15
20
25
30
35
75
/25
Ra
tio
of
Ne
t T
ota
l W
ea
lth
.4 .5 .6 .7 .8 .9Homeownership Rate
β = −73.0202∗∗∗ / R2 = 0.81 back
![Page 72: Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor Income, Taxes, Pensions I Labor income process logy(j,h) = y j +h with h+ = reh +#, #](https://reader033.fdocument.org/reader033/viewer/2022060706/6071e7c2049c343b9b5cd331/html5/thumbnails/72.jpg)
Total Population incl. Top 1%
DE
AT
FR
NL
LU
IT
FI
BE
GR
PT
SI
ES
.6.8
11
.21
.41
.61
.8G
E(0
) o
f N
et
To
tal W
ea
lth
.4 .5 .6 .7 .8 .9Homeownership Rate
β = −2.0186∗∗∗ / R2 = 0.86 back
![Page 73: Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor Income, Taxes, Pensions I Labor income process logy(j,h) = y j +h with h+ = reh +#, #](https://reader033.fdocument.org/reader033/viewer/2022060706/6071e7c2049c343b9b5cd331/html5/thumbnails/73.jpg)
Bottom 95% of the Population
DE
ATFR
NL
LU
IT
FI
BE
GR
PT
SIES
.6.8
11
.21
.41
.6G
E(0
) o
f N
et
To
tal W
ea
lth
.4 .5 .6 .7 .8 .9Homeownership Rate
β = −1.5445∗∗∗ / R2 = 0.85 back
![Page 74: Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor Income, Taxes, Pensions I Labor income process logy(j,h) = y j +h with h+ = reh +#, #](https://reader033.fdocument.org/reader033/viewer/2022060706/6071e7c2049c343b9b5cd331/html5/thumbnails/74.jpg)
Only Households with Positive Wealth
DE AT
FR
NL
LU
ITFI
BE
GR
PT
SIES
.6.8
11
.21
.41
.6G
E(0
) o
f N
et
To
tal W
ea
lth
.4 .5 .6 .7 .8 .9Homeownership Rate
β = −1.3132∗∗∗ / R2 = 0.74 back
![Page 75: Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor Income, Taxes, Pensions I Labor income process logy(j,h) = y j +h with h+ = reh +#, #](https://reader033.fdocument.org/reader033/viewer/2022060706/6071e7c2049c343b9b5cd331/html5/thumbnails/75.jpg)
Only Households Aged 65 or Younger
DE
AT
FR NL
LU
IT
FI
BE
GR
PT
SI
ES
.4.8
1.2
1.6
GE
(0)
of
Ne
t T
ota
l W
ea
lth
.4 .5 .6 .7 .8 .9Homeownership Rate
β = −1.8980∗∗∗ / R2 = 0.88 back
![Page 76: Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor Income, Taxes, Pensions I Labor income process logy(j,h) = y j +h with h+ = reh +#, #](https://reader033.fdocument.org/reader033/viewer/2022060706/6071e7c2049c343b9b5cd331/html5/thumbnails/76.jpg)
Income and Homeownership (OECD Data)
0.4 0.5 0.6 0.7 0.8 0.9 1
Homeownership Rate
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Gin
i of G
ross Incom
e
Data
Fitted Line: β = 0.064, R2 = 0.086
back
![Page 77: Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor Income, Taxes, Pensions I Labor income process logy(j,h) = y j +h with h+ = reh +#, #](https://reader033.fdocument.org/reader033/viewer/2022060706/6071e7c2049c343b9b5cd331/html5/thumbnails/77.jpg)
Calibration: Life-Cycle Income Profiles
20 30 40 50 60
Age j
0
0.2
0.4
0.6
0.8
1
1.2
1.4Labor
Incom
e P
rofile DE
AT
FR
NL
LU
IT
FI
BE
PT
GR
SI
ES
back
![Page 78: Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor Income, Taxes, Pensions I Labor income process logy(j,h) = y j +h with h+ = reh +#, #](https://reader033.fdocument.org/reader033/viewer/2022060706/6071e7c2049c343b9b5cd331/html5/thumbnails/78.jpg)
Calibration: Income Risk
Country σ2ε
Germany 0.05610Austria 0.04638France 0.05884Netherlands 0.04686Luxembourg 0.05914Italy 0.04591Finland 0.04706Belgium 0.06670Portugal 0.04120Greece 0.06001Slovenia 0.05604Spain 0.04280
back
![Page 79: Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor Income, Taxes, Pensions I Labor income process logy(j,h) = y j +h with h+ = reh +#, #](https://reader033.fdocument.org/reader033/viewer/2022060706/6071e7c2049c343b9b5cd331/html5/thumbnails/79.jpg)
Calibration: Taxes
Tax function: tc(y) =Tc(y)
y= tc
0 + tc1 ·
yi
yc + tc2 ·(
yi
yc
)φc
0 1 2 3 4 5 6 7 8
Multiples of Average Income
0
0.1
0.2
0.3
0.4
0.5
0.6
Avera
ge T
ax R
ate
R2 Germany =0.99904
R2 Italy =0.99983
R2 Spain =0.99982
Fitted Line Germany
Extrapolated Data Germany
Fitted Line Italy
Extrapolated Data Italy
Fitted Line Spain
Extrapolated Data Spain
back
![Page 80: Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor Income, Taxes, Pensions I Labor income process logy(j,h) = y j +h with h+ = reh +#, #](https://reader033.fdocument.org/reader033/viewer/2022060706/6071e7c2049c343b9b5cd331/html5/thumbnails/80.jpg)
Calibration: Pensions
Pension payments: pc(y) =
{ac
1yc + bc1yi if yi ≤ yc
ac2yc + bc
2yi if yi > yc
0 1 2 3 4 5 6
Multiples of Average Income
0
50
100
150
200
250
300
Re
lative
Pe
nsio
n L
eve
l
Fitted Line Germany
Data Germany
Fitted Line Italy
Data Italy
Fitted Line Spain
Data Spain
back
![Page 81: Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor Income, Taxes, Pensions I Labor income process logy(j,h) = y j +h with h+ = reh +#, #](https://reader033.fdocument.org/reader033/viewer/2022060706/6071e7c2049c343b9b5cd331/html5/thumbnails/81.jpg)
LTV Constraint
20 30 40 50 60
Age j
0
0.05
0.1
0.15F
rac. of H
om
eow
ners
at LT
V C
onstr
ain
t
Low s (Germany) Medium
s (Italy) High
s (Spain)
back
![Page 82: Rental Markets and Wealth Inequality in the Euro Area · 2018. 1. 24. · Calibration: Labor Income, Taxes, Pensions I Labor income process logy(j,h) = y j +h with h+ = reh +#, #](https://reader033.fdocument.org/reader033/viewer/2022060706/6071e7c2049c343b9b5cd331/html5/thumbnails/82.jpg)
Real Assets
20 22 24 26 28 30
Age j
0
0.2
0.4
0.6
0.8
1
1.2R
eal E
sta
te p
hh
Low s (Germany) Medium
s (Italy) High
s (Spain)
back
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Financial Assets
20 22 24 26 28 30
Age j
-0.4
-0.2
0
0.2F
inancia
l A
ssets
a (
Valu
e)
Low s (Germany) Medium
s (Italy) High
s (Spain)
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Net Wealth
20 22 24 26 28 30
Age j
0
0.2
0.4
0.6
0.8
1
Net W
ealth
Low s (Germany) Medium
s (Italy) High
s (Spain)
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Consumption
20 22 24 26 28 30
Age j
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5C
onsum
ption E
xpenditure
c
Low s (Germany) Medium
s (Italy) High
s (Spain)
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Shelter
20 22 24 26 28 30
Age j
0
0.5
1
1.5
2
2.5
Shelter
s (
Real U
nits)
Low s (Germany) Medium
s (Italy) High
s (Spain)
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Countries with Low Homeownership Rate
0.1
.2.3
.4.5
.6.7
Fra
ctio
n o
f P
op
ula
tio
n
0 .5 1 1.5 2 2.5 3 3.5 4Multiples of Group Average Wealth
Owners Renters
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Countries with Medium Homeownership Rate
0.1
.2.3
.4.5
.6.7
Fra
ctio
n o
f P
op
ula
tio
n
0 .5 1 1.5 2 2.5 3 3.5 4Multiples of Group Average Wealth
Owners Renters
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Countries with High Homeownership Rate
0.1
.2.3
.4.5
.6.7
Fra
ctio
n o
f P
op
ula
tio
n
0 .5 1 1.5 2 2.5 3 3.5 4Multiples of Group Average Wealth
Owners Renters
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A Decomposition in Levels
I Define for subgroups g = r, o:
WRcg = log
(wc
wcg
)and GEc
g = − 1Nc
g∑
i∈N cg
log
(wc
iwc
g
).
I Then we can write
GEc = HRc ·WRco + (1− HRc) ·WRc
r︸ ︷︷ ︸between group inequality
+ HRc · GEco + (1− HRc) · GEc
r︸ ︷︷ ︸within group inequality
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A Decomposition in Changes
I Define deviations from (simple) cross-country mean as
ωcg = WRc
g −WRg , γcg = GEc
g − GEg , ηc = HRc − HR
I We can write
∆GEc := GEc − GE = ∆cb + ∆c
w
with
∆cb = HR ·ωc
o + (1− HR) ·ωcr + ηc ·
[WRo −WRr
]+ ηc · [ωc
o −ωcr ]
∆cw = HR · γc
o + (1− HR) · γcr︸ ︷︷ ︸
Variation in GE
+ ηc ·[GEo − GEr
]︸ ︷︷ ︸Variation in HR
+ ηc · [γo − γr]︸ ︷︷ ︸Interaction
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A Decomposition in Changes
I Define deviations from (simple) cross-country mean as
ωcg = WRc
g −WRg , γcg = GEc
g − GEg , ηc = HRc − HR
I We can write
∆GEc := GEc − GE = ∆cb + ∆c
w
with
∆cb = HR ·ωc
o + (1− HR) ·ωcr + ηc ·
[WRo −WRr
]+ ηc · [ωc
o −ωcr ]
∆cw = HR · γc
o + (1− HR) · γcr︸ ︷︷ ︸
Variation in GE
+ ηc ·[GEo − GEr
]︸ ︷︷ ︸Variation in HR
+ ηc · [γo − γr]︸ ︷︷ ︸Interaction
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Between-Within Decomposition of Changes
Explains (in %)
Between ∆cb 36.1
Within ∆cw 63.9
Variation in GE 9.8Variation in HR 56.5Interaction −2.4
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