Rental Markets and Wealth Inequalityin the Euro Area

Fabian Kindermann and Sebastian Kohls

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

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?

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

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

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

The Data

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

Insight 1:

Many Rentersl

High Wealth Inequality

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

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

What it is not!

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

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

Insight 2:

Many Rentersl

Many Households with Low Wealth

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

Insight 3:

Renters are the Ones

to Hold Little Wealth

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

Insight 4:

Wealth is More Unequally Distributed

Among Renters Compared to the

Group of Homeowners

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

Insight 5:

In Countries with High Homeownership Rate,

Young Households Hold more Houses

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

Summary

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

A Quantitative Model

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

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, ∞]}

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

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.

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.

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

Calibration

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

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))

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

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

The Thought Experiment

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

Simulation Results

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

Model vs. Data 1:

Many Rentersl

High Wealth Inequality

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

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

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

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%

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%

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%

Model vs. Data 2:

Many Rentersl

Many Household with Low Wealth

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

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

Model vs. Data 3:

Wealth is More Unequally Distributed

Among Renters Compared to the

Group of Homeowners

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

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

Model vs. Data 4:

In Countries with High Homeownership Rate,

Young Households Hold more Houses

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

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

The Underlying Mechanism

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.

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

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)

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

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

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

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

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

Some Normative Statement

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

Conclusion

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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)

back

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)

back

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)

back

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)

back

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

back

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

back

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

back

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

back

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

back

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

back

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

back