Welfare%20effects%20of%20housing%20price%20appreciation%20in%20an%20economy%20with%20binding%20credit%20constraints

1
Welfare effects of housing price appreciation in
an economy with binding credit constraints

• Lecture presentation
• Ashot Tsharakyan
• April 2008

2
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

3
Introduction and motivation 1/5

• Considerable housing price appreciation in the
  developed countries during last decade,
  particularly in US

4
Introduction and motivation 2/5

• Existing research
• 1. the effects of housing price appreciation
  on households 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))

5
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

6
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

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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

8

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 d

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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

1 i.e households can borrow only up to fraction
mlt1 of total value of their housing stock
2 households can borrow as long as the gross
repayment next period does not exceed the next
periods expected monetary value of the
collateral.
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The households optimization problem ( case
with margin clause)
ct,ht1,bt1 s.t.




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Construction firms optimization problem

• where kK/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

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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 households
  optimization problem

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Definition of welfare adjustment

• Change in income necessary to keep households
  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)

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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,t0)

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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)

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Quantification of the result of exogenous
housing price model
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Endogenous price model Supply
side shocks 1/3

• Solve households and firms 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))

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

19
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 0.05
p 0.02 0.02
d 0.025 0.025
? 0.56 0.56
m - 0.8
ß 0.98 0.96
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Comparison of the welfare adjustment in
credit-constrained and unconstrained models 1/2

• Sensitivity analysis for different values of ?

? 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
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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 ?)
• What is the proper value for ? ?
• Use the fact that is
  the function of ? and parameters only
• Calibrate shares of housing and non-durable
  consumption in the households expenditures
  (shares available from CES by BLS)
• Calculate ? from the resulting equation
• The plausible range for ? is 0.56-0.64

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Endogenous price modelDemand-side shocks 1/5

• Changes in household income are straightforward
  demand shocks

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Endogenous price modelDemand-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

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Endogenous price modelDemand-side shocks 3/5

• Positive demand-side shock can also be generated
  by declines in the interest rates.

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Endogenous price modelDemand-side shocks 4/5
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Endogenous price modelDemand-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

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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

28
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

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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

30
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