Download Heterogeneity in cash-in

Welfare effects of housing price
appreciation in an economy with
binding credit constraints
Lecture presentation
Ashot Tsharakyan
April 2008
Presentation Outline










Introduction and motivation
The general model with endogenous housing price and binding
credit constraints
Special cases
Definition of welfare adjustment
The results of the model with exogenous housing price and binding
credit constraints
Endogenous housing price model: Supply-side shocks
Comparison of the welfare adjustment in credit-constrained and
unconstrained models
Endogenous housing price model: Demand-side shocks
US economy in 1995-2004: Actual aggregate welfare adjustment
Summary
Introduction and motivation 1/5
Considerable housing price appreciation in the developed
countries during last decade, particularly in US
Dynamics of housing prices in US from 1986 to 2004
Year
300,0
140,0
250,0
120,0
200,0
100,0
80,0
150,0
60,0
100,0
40,0
50,0
20,0
0,0
19
8
19 6
8
19 7
8
19 8
8
19 9
9
19 0
9
19 1
9
19 2
9
19 3
9
19 4
9
19 5
9
19 6
9
19 7
9
19 8
9
20 9
0
20 0
0
20 1
0
20 2
0
20 3
04
0,0
Year
Purchasing price
(thousands of dollars)
160,0
Index (percents)

Constatnt-quality
housing price index
(1996=100%)
Avergae purchasing
price of housing in
US (thousands of
dollars)
Introduction and motivation 2/5
Existing research:
1. the effects of housing price appreciation on household’s
consumption and welfare (Campbell and Cocco(2005),Li and
Yao(2004),Bajari et all(2005))
2. the effects of credit constraints on the housing market
behavior (Ortalo-Magne and Rady(2005))
Introduction and motivation 3/5

Bajari et all (2005) conclude that up to first order
approximation there are no effects of the housing price
appreciation on aggregate welfare

Two major limitations in their analysis:
1. The households are assumed to be not credit constrained
2. Housing price is given exogenously (no explicit equilibrium in
the housing market) and it appreciates due to unspecified
shocks

In Bajari et all (2005) the beneficial effect of housing price
appreciation which comes from relaxation of credit constraints
and better consumption smoothing, is ignored

The source of housing price appreciation should intuitively matter
for its eventual welfare effects
Introduction and motivation 4/5

In reality credit constraints are important drivers of the
housing market:
a) Empirical evidence: over 65% of owner-occupied housing
stock in US is mortgage financed, average actual LTV ratio in
US very close to maximum allowed LTV (constraints are
binding)
b) From modeling perspective, Ortalo-Magne and Rady (2005)
identify a crucial role of capital gains and losses experienced by
credit-constrained individuals in explaining housing market
fluctuations.

It should be important to model the source of housing
price appreciation that is to make housing price
endogenous
Introduction and motivation 5/5

First, aggregate welfare effects of housing price appreciation are
explored in exogenous price model with binding credit constraints

Then the endogenous price model is constructed in which housing
price appreciates due to different supply and demand side shocks

Change in building permit cost as a supply-side shifter (based on
Glaeser and Guyorko (2005) , changes in income and interest rates
as demand-side shifter

Endogenous price model is analyzed in both credit constrained and
unconstrained versions

Finally, cumulative aggregate welfare adjustment from the
considered combination of shocks is computed by aggregating the
results in credit constrained and unconstrained models
The model with endogenous housing price and
binding credit constraints 1/4

Housing price is determined endogenously and it changes
endogenously due to demand or supply shocks

Demand side is represented by the households and supply side
is represented by competitive sector of construction firms

Construction firms face CRS Cobb-Douglass technology (Amin
and Cappoza(1993)), use capital and land as inputs and need to
obtain building permit from zoning authority

Housing stock depreciates with constant rate δ
The model with endogenous housing
price and binding credit constraints 2/4
Possible forms of credit constraint:
 Margin clause (Mendoza and Durdu(2004))
bt 1  mqt ht 1

1
Kiyotaki-Moore constraint
2
(1  it 1 )bt 1  mEt qt 1ht 1
1 i.e
households can borrow only up to fraction m<1 of total value of their
housing stock
2 households can borrow as long as the gross repayment next period does
not exceed the next period’s expected monetary value of the collateral.
The household’s optimization
problem ( case with margin clause)
V (ht , bt , yt )  max{ u (ct , ht )  V (ht 1 , bt 1, yt 1 )}
{ct,ht+1,bt+1}
s.t.
ct  qt xt  st t  f 1{xt  0}  yt  it bt
bt 1  bt  st  bt
ht 1  ht  xt
bt 1  mqt ht 1
Construction firm’s optimization
problem
max   qt hs ,t  dkt  hs ,t n
s.t

hs ,t  (kt )
where k=K/L is capital to land ratio
n is the regulatory cost of obtaining building permit
(which is the source of endogenous housing price appreciation,
based on Glaeser and Guyorko(2005))
Profit-maximizing input is given by:
 qt  n 
kt  

d


(1 /(1 ))
Special cases

a) Model with exogenous housing price and credit-constrained
households:
Housing price is not determined endogenously. It is exogenous
and it is contained in the value function of the household as a
state. It appreciates due to non-specified shock
No construction firms in the model. Depreciation of housing is
abstracted from and it is assumed that fixed stock of housing is
traded

b) Model with endogenous housing price but binding credit
constraints
Credit constraint is removed from household’s optimization
problem
Definition of welfare adjustment

Change in income necessary to keep household’s lifetime
utility constant in case of housing price appreciation.
For the exogenous price model it is derived from the following
formula by solving for yt :
V (ht , bt , qt , yt )
V (ht , bt , qt , yt )
V 
qt 
yt  0
qt
yt
For the endogenous price model it is derived from the following
formula by solving for  y (case of change in building permit
cost)
V (hss , bss , yss )
V (hss , bss , yss )
V 
n 
y  0
n
y
The results of the model with exogenous housing
price and binding credit constraints

Individual welfare adjustment is given by the following
expression :
yt  xt qt  mht 1qt

Comparison with Bajari at al (2005) result :
a) Welfare loss is lower (welfare gain is higher) because of
the additional beneficial effect of housing price appreciation
in form of relaxation of binding credit constraints.
b) Homeowners do get a certain benefit from housing price
appreciation even without participating in housing
transactions (when xj,t=0)
Aggregate welfare adjustment

Aggregate welfare adjustment is the sum of individual
adjustments

When summing up across households the first term drops out
based on market clearing and aggregate welfare adjustment is
given by :

Wt   j  mh j ,t 1 qt

IMPORTANT FINDING
The housing price appreciation in the economy subject
to binding credit constraint implies improvement in the
aggregate welfare (in case of exogenous housing price
assumption)
Quantification of the result of
exogenous housing price model
Per household change in aggregate welfare in the economy
with binding credit constraints
1600
Welfare change(dollars)
1400
1200
1000
Per household change in
aggregate welfare(2003
dollars)
800
600
400
200
0
1995 1996 1997 1998 1999 2000 2001 2002 2003
Year
Endogenous price model:
Supply side shocks 1/3

Solve household’s and firm’s problem, define equilibrium,
derive steady state ,analyze what happens in the steady state
when building permit cost increases.

Assume special case utility function of modified CobbDouglass form (Li and Yao (2004))
(c1 h )1
u (ct , ht ) 
1 
Endogenous price model:
Supply side shocks 2/3
The welfare adjustment resulting from change in building permit
cost in the model with credit constraints is given by:
 B 1  y ss  f 1{x ss  0}  



 
y  n ss


q  n  (1   )   1   
D

The welfare adjustment resulting from change in building permit
cost in the model without credit constraints is given by:
ss
ss


y

f
1
{
x
 0} 

ss
 ss

y  n (i     )
A

 q  n  (1   ) 
Endogenous price model:
Supply-side shocks 3/3

Under the reasonable values of parameters (given in the
table below) both of the welfare adjustments shown
previously are positive , implying welfare loss
Parameter
Value in
unconstrained model
Value in the model
with credit constraints
i
π
0.04
0.02
0.05
0.02
δ
ω
0.025
0.56
0.025
0.56
m
β
0.98
0.8
0.96
Comparison of the welfare adjustment in creditconstrained and unconstrained models 1/2

Sensitivity analysis for different values of ω
ω
Unconstrained
B
  (1   )  D
Constrained
i ss    
A
0.1
1.046781
0.121252
0.2
1.098154
0.274385
0.3
1.154829
0.473092
0.4
1.217672
0.740199
0.5
1.287749
1.11679
0.6
1.366385
1.685037
0.7
1.455248
2.636675
0.8
1.556474
4.546914
0.9
1.672835
8.291815
Comparison of the welfare adjustment in creditconstrained and unconstrained models 2/2

Relationship between welfare adjustments in the constrained
and unconstrained economies depends on relative weight of
housing in the utility function ( parameter ω)

What is the proper value for ω ?
ss
c
Use the fact that
is the function of ω and
ss
ss
q h
parameters only
Calibrate shares of housing and non-durable consumption in
the household’s expenditures (shares available from CES by
BLS)
Calculate ω from the resulting equation
The plausible range for ω is 0.56-0.64




Endogenous price model:
Demand-side shocks 1/5
Changes in household income are straightforward demand shocks
Joint dynamics of median household income and constant-quality
housing price index
50000
160.0
45000
140.0
40000
30000
100.0
25000
80.0
20000
60.0
15000
40.0
10000
20.0
5000
0
0.0
year
Percents
120.0
35000
19
8
19 6
8
19 7
8
19 8
8
19 9
9
19 0
9
19 1
9
19 2
9
19 3
9
19 4
9
19 5
9
19 6
9
19 7
9
19 8
9
20 9
0
20 0
0
20 1
0
20 2
0
20 3
04
2005 dollars

Real median
hosuehold income
(left axis)
Constant-quality
housing price
index(right axis)
Endogenous price model:
Demand-side shocks 2/5

Welfare adjustment resulting from housing price
appreciation driven by income changes in the
constrained model is given by:
B(1   )
B  1 y ss  f 1{xss  0} q 
yold
ynew  
yold   
ss
D
 D
Dq
y 

In the unconstrained model it is given by:
   ( y ss  f 1{xss  0}) q 
(1   )(i ss     )
ss
yold
ynew  
yo  (i     ) 
ss
A
Aq
y 
A
Endogenous price model:
Demand-side shocks 3/5
 Positive demand-side shock can also be generated by
declines in the interest rates.
Average effective interest rate on mortgages in US
14
12
8
Average effective interest
rate on mortgages
6
4
2
year
20
03
20
01
19
99
19
97
19
95
19
93
19
91
19
89
19
87
0
19
85
mortgage rate
10
Endogenous price model:
Demand-side shocks 4/5
Long term government bond yield
12
10
long term governemnt bond
yield
6
4
2
year
03
20
01
20
99
19
97
19
95
19
93
19
91
19
89
19
87
19
85
0
19
percents
8
Endogenous price model:
Demand-side shocks 5/5

Welfare adjustment resulting from housing price appreciation
driven by changes in the interest rates in the model with credit
constraint is given by:
1
 (q ss  n)(1   ) 
Bm
ss
ss
i
y 
( y  f 1{x  0})(1   )( m  m )i 
( y  f 1{x  0})1  ss

D 2
(
q

n
(
1


))



ss
ss
2
Welfare adjustment resulting from housing price appreciation
driven by changes in the interest rates in the unconstrained
model is given by:
 (1  )  (q ss  n)  (1   ) 
(i ss   )    (1  ) ss
  (i ss     ) ss
ss
ss
  i
y 
 ( y  f 1{x  0})  i 
 ( y  f 1{x  0})  
2
ss
A
A
 A  (q  n  (1   )) 
Endogenous price model:
Demand-side shocks vs supply-side shocks

Quantify welfare adjustments resulting from housing appreciation
driven by changes in income and interest rates using already set
values of parameters

The results show that those adjustments are negative implying that
housing price appreciation driven by changes in income and interest
rates leads to welfare improvement

As already shown, negative supply side shock in the form increase
in building permit cost leads to welfare loss

Modeling source of housing price appreciation is important
when considering the welfare effects of housing price
appreciation
US economy in 1995-2004: Actual
aggregate welfare adjustment 1/2

It is reasonable to expect that combination of demand and supply
shocks affected the real US economy and US housing market

Apply theoretical results to actual US economy, and calculate the
aggregate welfare effects of housing price appreciation driven by
combination of considered demand and supply shocks
for 1995-2004 (period of significant housing price growth)

Use US data to calculate changes in shock variables over the
considered period, calculate resulting welfare adjustments for
each shock and each model (credit-constrained and
unconstrained), sum them up over shocks for each group of
households
US economy in 1995-2004: Actual
aggregate welfare adjustment 2/2

Calibrate the weights of credit constrained and unconstrained
households in the economy, using data on net worth of US
households by the age of the household head (available from
Survey of Consumer Finance)

Aggregate over the calibrated weights the results for credit
constrained and unconstrained models to get final cumulative
aggregate welfare change

Result : Aggregate welfare improved, demand-side shocks
dominated during the considered period
Summary

In the exogenous housing price model with binding credit constraints
housing price appreciation implies an improvement in aggregate welfare.

The result is due to the fact that credit-constrained model takes into
account the welfare improving effect of the housing price appreciation,
which implies relaxation of binding credit constraints.

In the model with endogenous housing price, welfare effect of housing
price appreciation depends on whether it is caused by demand-side shock
or supply-side shock

The relationship between supply-driven welfare adjustments in the two
modeling alternatives depends on the relative weight housing in the
agent.s utility function

The calculation of cumulative aggregate welfare adjustment shows that
demand-side shocks dominated in US economy and aggregate welfare
improved