Welfare effects of housing Welfare effects of housing price appreciation in an price appreciation in an

economy with binding credit economy with binding credit constraintsconstraints

LectureLecture presentation presentation

Ashot Tsharakyan Ashot Tsharakyan April 2008April 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

0,0

20,0

40,0

60,080,0

100,0

120,0

140,0

160,0

1986

1987

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1989

1990

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2004

Year

Inde

x (p

erce

nts)

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Year

Purc

hasi

ng p

rice

(thou

sand

s of

dol

lars

) Constatnt-qualityhousing price index(1996=100%)

Avergae purchasingprice of housing inUS (thousands ofdollars)

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

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 1/4

The model with endogenous housing price and binding credit constraints 2/4

Possible forms of credit constraint: Margin clause (Mendoza and Durdu(2004)) 1

Kiyotaki-Moore constraint 2

11 ttt hmqb

1111)1( ttttt hqmEbi1 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)

)},(),(max{),,( 1,11 tttttttt ybhVhcuybhV

tttttttt biyxfsxqct

}0{1

tttt bsbb 1

ttt xhh 1

11 ttt hmqb

{ct,ht+1,bt+1}

s.t.

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:

ts

nhdkhq tsttst

.

max ,,

)(, tts kh

))1/(1(

dnqk t

t

Construction firm’s optimization problem

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 :

For the endogenous price model it is derived from the following formula by

solving for (case of change in building permit cost)

0),,,(),,,(

t

t

ttttt

t

tttt yy

yqbhVqq

yqbhVV

0),,(),,(

y

yybhVn

nybhVV ssssssssssss

ty

y

The results of the model with exogenous housing price and binding credit constraints

Individual welfare adjustment is given by the following expression :

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)

ttttt qmhqxy 1

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 :

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)

j tjt qmhWt 1,

Quantification of the result of exogenous housing price model

Per household change in aggregate welfare in the economy with binding credit constraints

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200

400

600

800

1000

1200

1400

1600

1995 1996 1997 1998 1999 2000 2001 2002 2003

Year

Wel

fare

cha

nge(

dolla

rs)

Per household change inaggregate welfare(2003dollars)

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 Cobb-Douglass form (Li and Yao (2004))

1)(),(

11 hchcu tt

The welfare adjustment resulting from change in building permit

cost in the model with credit constraints is given by:

The welfare adjustment resulting from change in building permit cost in the model without credit constraints is given by:

Endogenous price model: Supply side shocks 2/3

DxfyB

nqny

ssss

ss

}0{11

1)1(

)1(}0{1)(

nqA

xfyiny ss

ssssss

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 0.04 0.05π 0.02 0.02δ 0.025 0.025ω 0.56 0.56m - 0.8β 0.98 0.96

Comparison of the welfare adjustment in credit-constrained and unconstrained models 1/2

Sensitivity analysis for different values of ω

Ai ss

DB

)1(

ω Unconstrained Constrained

 

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 credit-constrained 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 ? Use the fact that is the function of ω and

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

ssss

ss

hqc

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

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10000

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20000

25000

30000

35000

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50000

year

2005

dol

lars

0.0

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Perc

ents Real median

hosuehold income(left axis)

Constant-qualityhousing priceindex(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:

In the unconstrained model it is given by:

oldssss

ss

oldnew yyq

Dqxfy

DBy

DBy

}0{11)1(

oldssss

ssss

o

ss

new yyq

Aqxfy

Aiy

Aiy

})0{1()())(1(

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

0

2

4

6

8

10

12

14

year

mor

tgag

e ra

te

Average effective interestrate on mortgages

Endogenous price model:Demand-side shocks 4/5

Long term government bond yield

0

2

4

6

8

10

12

year

perc

ents

long term governemnt bondyield

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:

Welfare adjustment resulting from housing price appreciation driven by changes in the interest rates in the unconstrained model is given by:

inqnqxfy

DBmimmxfyy ss

ssssssssss

))1(()1)((1})0{1())(1})(0{1(1

22

inqAnq

xfyA

iixfy

Ai

y ss

ssssss

ssssss

ss

))1(()1()()1(

})0{1()(

})0{1()1()(

2

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