Lecture 3
Fall 2009
Referee Reports
Referee Reports
Housing Data
U.S. Housing Data
•
Housing price movements unconditionally
Census data
Transaction/deed data (provided by government agencies or available
via public records)
Household data (PSID, Survey of Consumer Finances, etc.)
Mortgage data (appraised value of the home)
•
Repeat sales indices
OFHEO
Case-Shiller
Repeat Sales vs. Unconditional Data
•
House prices can increase either because the value of the land under the
home increases or because the value of the structure increases.
*
Is home more expensive because the underlying land is worth more
or because the home has a fancy kitchen.
•
Often want to know the value of the land separate from the value of the
structure.
•
New homes often are of higher quality than existing homes.
•
Repeat sales indices try to difference out “structure” fixed effects –
isolating the effect of changing land prices.
*
Assumes structure remains constant (hard to deal with home
improvements).
OFHEO/FHFA Repeat Sales Index
•
OFHEO – Office of Federal Housing Enterprise Oversight
FHFA – Federal Housing Finance Agency
Government agencies that oversee Fannie Mae and Freddie Mac
•
Uses the stated transaction price from Fannie and Freddie mortgages to
compute a repeat sales index. (The price is the actual transaction price
and comes directly from the mortgage document)
•
Includes all properties which are financed via a conventional mortgage
(single family homes, condos, town homes, etc.)
•
Excludes all properties financed with other types of mortgages (sub
prime, jumbos, etc.)
•
Nationally representative – creates separate indices for all 50 states and
over 150 metro areas.
Case Shiller Repeat Sales Index
•
Developed by Karl Case and Bob Shiller
•
Uses the transaction price from deed records (obtained from public
records)
•
Includes all properties regardless of type of financing (conventional, sub
primes, jumbos, etc.)
•
Includes only single family homes (excludes condos, town homes, etc.)
•
Limited geographic coverage – detailed coverage from only 30 metro
areas. Not nationally representative (no coverage at all from 13 states –
limited coverage from other states)
•
Tries to account for the home improvements when creating repeat sales
index (by down weighting properties that increase by a lot relative to
others within an area).
-5.00%
Jan-92
Aug-92
Mar-93
Oct-93
May-94
Dec-94
Jul-95
Feb-96
Sep-96
Apr-97
Nov-97
Jun-98
Jan-99
Aug-99
Mar-00
Oct-00
May-01
Dec-01
Jul-02
Feb-03
Sep-03
Apr-04
Nov-04
Jun-05
Jan-06
Aug-06
Mar-07
Oct-07
May-08
Dec-08
Jul-09
OFHEO vs. Case Shiller: National Index
20.00%
15.00%
10.00%
5.00%
0.00%
-10.00%
-15.00%
-20.00%
-25.00%
-30.00%
CS Composite 10
CS Composite 20
OFHEO
OFHEO vs. Case Shiller: L.A. Index
0.3
0.2
0.1
0
-0.1
-0.2
-0.3
-0.4
LA-CS
LA-OFHEO
0.15
OFHEO vs. Case Shiller: Denver Index
0.1
0.05
0
-0.05
-0.1
-0.15
Denver-CS
Denver-OFHEO
0.1
OFHEO vs. Case Shiller: Chicago Index
0.05
0
-0.05
-0.1
-0.15
-0.2
-0.25
Chicago-CS
Chicago-OFHEO
OFHEO vs. Case Shiller: New York Index
0.15
0.1
0.05
0
-0.05
-0.1
-0.15
NY-CS
NY-OFHEO
Conclusion: OFHEO vs. Case - Shiller
• Aggregate indices are very different but MSA indices are nearly identical.
• Does not appear to be the result of different coverage of properties included.
• I think the difference has to do with the geographic coverage.
• If using MSA variation, does not matter much what index is used.
• If calibrating aggregate macro models, I would use OFHEO data instead of
Case-Shiller – I think it is more representative of the U.S.
A Note on Census Data
•
To assess long run trends in house prices (at low frequencies), there is nothing
better than Census data.
•
Very detailed geographic data (national, state, metro area, zip code, census
tract).
•
Goes back at least to the 1940 Census.
•
Have very good details on the structure (age of structure, number of rooms,
etc.).
•
Can link to other Census data (income, demographics, etc.).
Housing Cycles
Average Annual Real Housing Price Growth By US State
State
AK
AL
AR
AZ
CA
CO
CT
DC
DE
FL
GA
HI
IA
ID
IL
IN
1980-2000
-0.001
0.000
-0.009
-0.002
0.012
0.012
0.012
0.010
0.011
-0.002
0.008
0.004
-0.001
-0.001
0.010
0.002
2000-2007
0.041
0.024
0.023
0.061
0.066
0.012
0.044
0.081
0.053
0.068
0.019
0.074
0.012
0.047
0.030
0.020
Average
0.011
0.036
State
MT
NC
ND
NE
NH
NJ
NM
NV
NY
OH
OK
OR
PA
RI
SC
SD
1980-2000
0.003
0.008
-0.010
-0.002
0.014
0.015
-0.002
-0.005
0.020
0.003
-0.019
0.009
0.008
0.017
0.007
0.002
2000-2007
0.049
0.022
0.033
0.007
0.041
0.058
0.043
0.060
0.051
-0.001
0.019
0.051
0.042
0.059
0.025
0.025
17
Typical “Local” Cycle
New York State: Real Housing Price Growth
0.200
0.150
0.100
0.050
0.000
-0.050
-0.100
-0.150
HPI-Growth-Real
18
Typical “Local” Cycle
0.250
California: Real Housing Price Growth
0.200
0.150
0.100
0.050
0.000
-0.050
-0.100
-0.150
HPI-Growth-Real
19
Housing Cycles: Part 1
U.S. Metro Area Data, (1980 - 1990 vs. 1990 - 2000)
Real House Price Changes
0.60
0.50
0.40
y = -0.3798x + 0.0027
R² = 0.3804
0.30
0.20
0.10
0.00
-0.10
-0.20
-0.30
-0.40
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
20
1
Housing Prices and Housing Cycles (Hurst and Guerrieri (2009))
• Persistent housing price increases are ALWAYS followed by persistent
housing price declines
Some statistics about U.S. metropolitan areas 1980 – 2000
• 44 MSAs had price appreciations of at least 15% over 3 years during this
period.
• Average price increase over boom (consecutive periods of price increases):
55%
• Average price decline during bust (the following period of price declines):
30%
• Average length of bust: 26 quarters (i.e., 7 years)
• 40% of the price decline occurred in first 2 years of bust
21
1976
1977
1978
1979
1981
1982
1983
1984
1986
1987
1988
1989
1991
1992
1993
1994
1996
1997
1998
1999
2001
2002
2003
2004
2006
2007
2008
OFHEO House Price Index
Typical “Country” Cycle (US – OFHEO Data)
0.20
-0.10
U.S. Nominal House Price Appreciation: 1976 - 2008
0.15
0.10
0.05
0.00
-0.05
22
Typical “Country” Cycle (US – OFHEO Data)
0.12
U.S. Real House Price Appreciation: 1976 - 2008
0.09
0.06
0.03
0.00
-0.03
-0.06
-0.09
-0.12
23
Average Annual Real Price Growth By OECD Country
Country
1970-1999
2000-2006
Country
1970-1999
2000-2006
U.S.
Japan
Germany
France
Great Britain
Italy
Canada
Spain
Australia
0.012
0.010
0.001
0.010
0.022
0.012
0.013
0.019
0.015
0.055
-0.045
-0.029
0.075
0.068
0.051
0.060
0.081
0.065
Netherlands
Belgium
Sweden
Switzerland
Denmark
Norway
Finland
New Zealand
Ireland
0.023
0.019
-0.002
0.000
0.011
0.012
0.009
0.014
0.022
0.027
0.064
0.059
0.019
0.065
0.047
0.040
0.080
0.059
1970-1999
2000-2006
0.012
0.046
Average
24
Country Cycles – The U.S. is Not Alone
Real House Price Growth
UK: 1978 - 2006
0.250
0.200
0.150
0.100
0.050
0.000
-0.050
-0.100
-0.150
25
Country Cycles – The U.S. is Not Alone
Real House Price Growth
Italy: 1978 - 2006
0.250
0.200
0.150
0.100
0.050
0.000
-0.050
-0.100
-0.150
26
Country Cycles – The U.S. is Not Alone
Real House Price Growth
Japan: 1978 - 2006
0.120
0.100
0.080
0.060
0.040
0.020
0.000
-0.020
-0.040
-0.060
-0.080
27
Housing Cycles: Part 2
OECD Country Level Data (1970 - 2000)
Price Changes in Booms vs. Subsequent Busts
0
-0.1
y = -0.6185x + 0.0584
R² = 0.483
Size of Subsequent Bust
-0.2
-0.3
-0.4
-0.5
-0.6
-0.7
0
0.2
0.4
0.6
Size of Boom
0.8
28
1
Do Supply Factors Explain 2000-2008 Cycle
.04
Change in Total Housing Units Against Change in Housing Price
Adjusted for Population Changes (2000-2005, State Level)
ND MN
IN
NC
WI
GA
LA
SCIA
MS SD
MI
AL
KS
OH
NE
ID
KY
TN
WV
IL
ARMO
UT
OK
NM
TX
-.02
0
.02
CO
NV
VA
FL
WY
WA
DE VT
PA
ME
NH MA
OR
NY
AZ
MT
CT
NJ MD
CA
RI
DC
-.04
AK
HI
-.2
0
Residuals
.2
Residuals
.4
.6
Fitted values
29
Do Supply Factors Explain 2000-2008 Cycle
Change in Total Housing Units Against Change in Housing Price
Adjusted for Population Changes (2005-2009, State Level)
.02
NV
FL
.01
HI
0
MI
RI
-.01
CA
AZ
ND
ME
AL
SC
NJ
ID
MD
VA
NH
VT
DE
MS
GA WICO
AR TN
MNOH IL
WA
WV SD
NC
NE IA
NM
CT
TX
IN
KY
MO
PA
OR
KS
MA
DC
OK
NY
UT
WY
AK
-.02
MT
-.03
LA
-.6
-.4
-.2
Residuals
Residuals
0
.2
Fitted values
30
Homework
Why Do Housing Prices Cycle?
A Spatial Equilibrium
Model
Part 1
Model Particulars (Baseline Model): The City
• City is populated by N identical individuals.
• City is represented by the real line such that each point on the line (i) is a
different location:
i  (, )
• nt (i ) :
• ht (i ) :

Measure of agents who live in i.
Size of the house chosen by agents living in i.
•

•
nt (i )ht (i )  1

nt (i)di  N
(market clearing condition)
(maximum space in i is fixed and
normalized to 1)
33
Household Preferences
Static model:
max c(i ) h(i) 
 > 0 and  > 0
c(i )  R(i )h(i)  Y
normalize price of consumption to 1
ct , ht ,i
Arbitrage implies:
1
Pt (i )  R(i ) 
Pt 1 (i )
1 r
Construction
A continuum of competitive builders can always build a unit of housing
at constant marginal cost  .
Profit maximization implies builders will build a unit of housing anytime:
Pt  
Demand Side of Economy
max c(i ) h(i )   [Y  c(i )  R(i ) h(i)]


c
(
i
)
h
(
i
)
 c(i ) 1 h(i )   

c(i )
 c(i ) h(i )  1
c(i ) h(i ) 

  R (i )
h(i )
 h(i ) 
h(i )
1


 c(i )  (Y  R (i )h(i )) R(i )
(F.O.C. wrt c)
(F.O.C. wrt h)
Housing and Consumption Demand Functions

 1 
h(i ) 
Y

(   )  R(i ) 
c(i ) 

(   )
Y
Spatial Equilibrium
Households have to be indifferent across locations:
Consider two locations i and %
i.
Spatial indifference implies that:
c(i ) h(i )   c(%
i ) h(%
i )





       1 
       1 
Y
Y








 Y 
 Y  %
   
   
   
   
 R (i ) 
 R (i ) 
R(i )  R(%
i)
for all i and %
i

Equilibrium
r
R (i ) 
P (i )
(1  r )
Housing Demand Curve:
    1 r  1 
h(i )=h = 
 
Y 



r
 P 

 
Housing Supply Curve:
P=
Graphical Equilibrium
ln(P)
hD(Y)
ln(κ) =
ln(P*)
ln(h*)
ln(h)
Shock to Income (similar to shock to interest rate)
hD(Y1)
ln(P)
hD(Y)
ln(κ) =
ln(P*)
ln(h*)
ln(h*1) ln(h)
Shock to Income (with adjustment costs to supply)
hD(Y1)
ln(P)
hD(Y)
ln(κ) =
ln(P*)
ln(h*)
ln(h*1) ln(h)
Some Conclusions (Base Model)
•
If supply is perfectly elastic in the long run (land is available and
construction costs are fixed), then:
Prices will be fixed in the long run
Demand shocks will have no effect on prices in the long run.
Short run amplification of prices could be do to adjustment costs.
Model has “static” optimization. Similar results with dynamic
optimization (and expectations – with some caveats)
•
Notice – location – per se – is not important in this analysis. All locations
are the same.
Equilibrium with Supply Constraints
Suppose city (area broadly) is of fixed size (2*I). For illustration, lets index
the middle of the city as (0).
-I
0
I
Lets pick I such that all space is filled in the city with Y = Y and r = r.
2I = N (h(i)*)
    1 r  1 
2I  N 
 
 Y  



r

 P 


 N     1 r 
P   

 Y  
 2I        r 
Comparative Statics
What happens to equilibrium prices when there is a housing demand shock (Y
increases or r falls).
Focus on income shock. Suppose Y increases from Y to Y1. What happens to
prices?
 N     1 r 
P   

 Y  
 2I        r 
  N    1 r  
ln( P )  ln    
   ln(Y )

  2I        r  
With inelastic housing supply (I fixed), a 1% increase in income leads to a 1%
increase in prices (given Cobb Douglas preferences)
Shock to Income With Supply Constraints
ln(P1)
ln(κ) =
ln(P)
hD(Y1)
hD(Y)
ln(h)=ln(h1)
ln(h)
The percentage change in income = the percentage change in price
Intermediate Case: Upward Sloping Supply
ln(P1)
ln(κ) =
ln(P)
hD(Y1)
hD(Y)
ln(h)=ln(h1)
ln(h)
Cost of building in the city increases as “density” increases
Implication of Supply Constraints (base model)?
•
The correlation between income changes and house price changes should
be smaller (potentially zero) in places where density is low (N h(i)* < 2I).
•
The correlation between income changes and house price changes should
be higher (potentially one) in places where density is high.
•
Similar for any demand shocks (i.e., decline in real interest rates).
Question:
Can supply constraints explain the cross city differences
in prices?
Topel and Rosen (1988)
“Housing Investment in the United States” (JPE)
•
First paper to formally approach housing price dynamics.
•
Uses aggregate data
•
Finds that housing supply is relatively elastic in the long run
Long run elasticity is much higher than short run elasticity.
Long run was about “one year”
•
Implication:
Long run annual aggregate home price appreciation
for the U.S. is small.
Comment 1: Cobb Douglas Preferences?
•
Implication of Cobb Douglas Preferences:
  
1
h
Y
  



R


  
Rh  
 Y 
   
(expenditure on housing)
Implication: Constant expenditure share on housing
Implication: Housing expenditure income elasticity = 1
ln(Rh) = 0  1 ln(Y )  
Estimated 1 should be 1
Use CEX To Estimate Housing Income Elasticity
•
Use individual level data from CEX to estimate “housing service” Engel
curves and to estimate “housing service” (pseudo) demand systems.
Sample:
NBER CEX files 1980 - 2003
Use extracts put together for “Deconstructing Lifecycle
Expenditure” and “Conspicuous Consumption and Race”
Restrict sample to 25 to 55 year olds
Estimate:
(1)
(2)
*
*
*
ln(ck) = α0 + α1 ln(tot. outlays) + β X + η
(Engle Curve)
sharek = δ0 + δ1 ln(tot. outlays) + γ X + λ P + ν (Demand)
Use Individual Level Data
Instrument total outlays with current income, education, and occupation.
Total outlays include spending on durables and nondurables.
51
Engel Curve Results (CEX)
Dependent Variable
log rent (renters)
log rent (owners)
log rent (all)
Coefficient
S.E.
0.93
0.84
0.94
0.014
0.001
0.007
* Note: Rent share for owners is “self reported” rental value of home
Selection of renting/home ownership appears to be important
52
Demand System Results (CEX)
Dependent Variable
rent share (renters, mean = 0.242)
rent share (owners, mean = 0.275)
rent share (all, mean = 0.263)
Coefficient
S.E.
-0.030
-0.050
-0.025
0.003
0.002
0.002
* Note: Rent share for owners is “self reported” rental value of home
Selection of renting/home ownership appears to be important
53
Engel Curve Results (CEX)
Dependent Variable
log rent (renters)
log rent (owners)
log rent (all)
Coefficient
S.E.
0.93
0.84
0.94
0.014
0.001
0.007
* Note: Rent share for owners is “self reported” rental value of home
Selection of renting/home ownership appears to be important
Other Expenditure Categories
log entertainment (all)
log food (all)
log clothing (all)
1.61
0.64
1.24
0.013
0.005
0.010
X controls include year dummies and one year age dummies
54
Demand System Results (CEX)
Dependent Variable
rent share (renters, mean = 0.242)
rent share (owners, mean = 0.275)
rent share (all, mean = 0.263)
Coefficient
S.E.
-0.030
-0.050
-0.025
0.003
0.002
0.002
* Note: Rent share for owners is “self reported” rental value of home
Selection of renting/home ownership appears to be important
Other Expenditure Categories
entertainment share (all, mean = 0.033) 0.012
food share (all, mean = 0.182)
-0.073
clothing share (all, mean = 0.062)
0.008
0.001
0.001
0.001
X controls include year dummies and one year age dummies
55
Comment 1: Conclusion
• Cannot reject constant income elasticity (estimates are pretty close to 1 for
housing expenditure share).
• Consistent with macro evidence (expenditure shares from NIPA data are
fairly constant over the last century).
• If constant returns to scale preferences (α+β = 1), β ≈ 0.3 (share of
expenditure on housing out of total expenditure).
Comment 2: Cross City Differences
“On Local Housing Supply Elasticity” Albert Siaz (QJE Forthcoming)
• Estimates housing supply elasticities by city.
• Uses a measure of “developable” land in the city.
• What makes land “undevelopable”?
Gradient
Coverage of water
• Differences across cities changes the potential supply responsiveness across
cities to a demand shock (some places are more supply elastic in the short
run).
Comment 3: Are Housing Markets Efficient?
• Evidence is mixed
• Things to read:
“The Efficiency of the Market for Single-Family Homes” (Case and Shiller,
AER 1989)
“There is a profitable trading rule for persons who are free to time the
purchase of their homes. Still, overall, individual housing price changes are
not very forecastable.”
Subsequent papers find mixed evidence:
Transaction costs?
Comment 4: Can Supply Constraints Explain
Cycles?
“Housing Dynamics” (working paper 2007) by Glaeser and Gyrouko
Calibrated spatial equilibrium model
Match data on construction (building permits) and housing prices using time
series and cross MSA variation.
Find that supply constraints cannot explain housing price cycles.
Their explanation:
Negatively serially correlated demand shocks.
What Could Be Missing?
• Add in reasons for agglomeration.
• Long literature looking at housing prices across areas with agglomeration.
• Most of these focus on “production” agglomerations.
• We will lay out one of the simplest models – Muth (1969), Alonzo (1964),
Mills (1967)
• Locations are no longer identical. There is a center business district in the
area where people work (indexed as point (0) for our analysis).
• Households who live (i) distance from center business district must pay
additional transportation cost of τi.
Same Model As Before – Except Add in Transport Costs
Static model:
max c(i ) h(i ) 
ct , ht ,i
 > 0 and  > 0
c(i )  R (i )h(i )  Y   i
Still no supply constraints (unlimited areas)
Demand Side of Economy
max c(i ) h(i )   [Y   i  c(i )  R(i ) h(i )]


c
(
i
)
h
(
i
)
 c(i ) 1 h(i )   

c(i )
 c(i ) h(i )  1



c(i ) h(i ) 

  R (i )
h(i )
 h(i )   
h(i )
1
 


 c(i )    (Y   i  R (i ) h(i )) R (i )
(F.O.C. wrt c)
(F.O.C. wrt h)
Housing and Consumption Demand Functions

 1 
h(i ) 
(Y   i ) 

(   )
 R (i ) 
c(i ) 

(   )
(Y   i )
Spatial Equilibrium
Households have to be indifferent across locations:
Consider two locations i and %
i.
Spatial indifference implies that:
c (i ) h(i )   c(%
i ) h(%
i )
 

Y   i 
 
%
i 
R (%
i )  R (i )
Y   
%
When i > %
i, R(i) < R(i)
Equilibrium
Equilibrium Result:
All occuppied neighborhoods i will be contained in [-I,I].
Define R(I) and P(I) as the rent and price, respectively,
at the boundary of the city.
Given arbitrage, we know that:
r
R(I) =

(1  r )
 

Y   i 
 
Y   I  
r
  R (i )
(1  r )
Complete Equilibrium: Size of City (Solve for I)

Remember:
h(i)n(i) = 1
and

n(i ) di  N
i 
 1 
2 
di  N
h(i ) 
i 0 
I
 
h(i )  
  
 
 1  r   1 
  r     Y   I   (Y   i )
 



Some Algebra (if my algebra is correct…)

I 
1
2 


 



1  r   1 
i 0
 (Y   i ) 
 
Y


I


  r   



 



I


N
(Y   i ) di 

2
i 0


di  N



 
   1  r   1 
      r     Y   I  
 



 N 1  r   1 
  

 1
1





2  r   
1


I    (Y )

 
 N 1  r   1 
  
 2  r      1

 


Prices By Distance (Initial Level of Y = Y0)
P
κ
0
I0
i
Linearized only for graphical illustration
Prices fall with distance. Prices in essentially all locations exceed marginal cost.
Suppose Y increases from Y0 to Y1
P
κ
0
I0
I1
i
Even when supply is completely elastic, prices can rise permanently with a
permanent demand shock.
A Quick Review of Spatial Equilibrium Models
• Cross city differences?
Long run price differences across cities with no differential
supply constraints.
Strength of the center business district (size of τ) drives long
run price appreciations across city.
• Is it big enough?
• Fall in τ will lead to bigger cities (suburbs) and lower prices in
center city (i = 0).