Transcript 7500_l_19_Things_wHP

Things to do with Hedonic Prices
© Allen C. Goodman, 2009
Things to do …
1. Estimate them
2. Interpret them
3. Make price indices
Value v. # of Rooms
Value  a  b * Rooms
300000
250000
Value
200000
150000
100000
50000
0
0.00
2.00
4.00
6.00
8.00
10.00
Number of Rooms
12.00
14.00
Interpret them (1)
P = 0 +  1Z1 +  2Z2 + ... + t + ,
1. Estimate price changes
Coefficient on t term would provide “quality adjusted price.”
Problems:
a. Estimating it this way assumes that  terms are
constant both absolutely and relatively.
b.  terms may actually vary across areas.
Interpret them (2)
P = 0 +  1Z1 +  2Z2 + ... + t + ,
1. Use them for property assessment.
Suppose we have a data base on all of the houses in an area.
H1 = (6 rooms, 2000 sq.ft., 10000 sq. ft. lot, etc.)
H2 = (5 rooms, 1000 sq.ft., 8000 sq. ft. lot, etc.)
H3 = (7 rooms, 3000 sq.ft., 15000 sq. ft. lot, etc.)
We estimate regression on house sales in the area and we get:
Pˆ1  a  b * 6  c * 2000  d * 10000
Pˆ  a  b * 5  c *1000  d * 8000
2
Pˆ3  a  b * 7  c * 3000  d *15000
Problems
• Do current sales reflect all of the housing?
• Do we know enough about all of the houses
to make them comparable?
Interpret them (3) – air pollution
• This is a logical succession to the discussions of
hedonic price models. The arguments went
something like this:
• If air pollution was bad, then people should be
willing to pay less for property that was polluted.
• If this was the case, then this should give some
measure of the benefits that occur from the
alleviation of air pollution.
• It should also give you the increase in property
values that might occur, if we have an alleviation
of pollution.
Air pollution
So we get:
Problems with this:
1. To measure benefits,
you want to measure the
area under a demand
curve.
We can see from the accompanying diagram, that any
particular hedonic price
gives you only one point
on the demand curve.
Valuation
P/zi
0
zi
% of Clean Air
100
Air pollution
So we get:
Problems with this:
1. To measure benefits,
you want to measure the
area under a demand
curve.
We can see from the accompanying diagram, that any
particular hedonic price
gives you only one point
on the demand curve.
Estimated
Valuation
P/Zi
True
0
zi
% of Clean Air
100
Air pollution
Problems with this:
2. As we mentioned earlier,
we have a real problem
Valuation
with the "open city closed city" question.
If pollution abatement
P/Zi
changes the supply of
different types of land, the
total land values might not
change much.
Estimated
0
zi
% of Clean Air
100
Other problems …
3. We really don't know what effects pollution should really
have on property values. Does twice as much pollution
just look bad, is it twice as bad, or does it kill you?
Ridker and Henning used census tract level data, for 1960, in
St. Louis. They looked at median property value in the
tract. Used a variety of explanatory variables -- for air
pollution, they used sulfates.
They found that a 1 unit fall in sulfates was correlated with a
$245 rise in property value. This implies, they said, an
increase in property values by approximately $83,000,000
(in $1960 - multiply by 5 for current dollars --- > about
$415,000,000).
Then use the identity:
V = R/i to determine annual gain. If i = 10%, then:
83,000,000 = R/0.1  R = 8,300,000.
Create Price Indices
P = 0 +  1Z1 +  2Z2 + ... +  ,
Example:
Suppose we have reason to believe that there are two
submarkets. We estimate:
P1 = 10 + 11Z1 + 12Z2 + ... +
P2 = 20 + 21Z1 + 22Z2 + ... +
Take a bundle with (Z1*, Z2*, …) and “move” it from
submarket to submarket. It is presumably always the same
house.
P1* = 10 + 11Z1* + 12Z2* + ... +
P2* = 20 + 21Z1* + 22Z2* + ... +
Price index = P1* / P2*
Create Quantity Indices
P1* = 10 + 11Z1* + 12Z2* + ... +
P2* = 20 + 21Z1* + 22Z2* + ... +
Price index = P1* / P2*
Q1 = P1/P1*
So if a house has a price of $250,000, and the “index
house” has P1* = 200,000. The particular house
has 1.25 (= 250/200) units of “housing.”
Repeat Sale Indices
Pint =  + βX + γAge + Σj δjDj + εint
Where Dj is a set of year dummies for when houses
were built.
Error term ε is
ε int = ρn + κt + λage + μint
where ρn is house specific κt is year specific, λage is
related to house age and μ is uncorrelated
Repeat Sale (2)
Resale method with one year lag nets out house-specific
effects yielding:
ΔP= Pint – Pint-1 = γ + (κt – κt-1) + (λ age+1 – λage).
This makes several assumptions
1. β is constant year after year – critical assumption.
2. λ is homoskedastic (GT show otherwise).
Case-Shiller and others don’t do single period lags only.
They difference by various intervals and argue that
the differences are heteroskedastic by length of
interval.
GT
• Goodman-Thibodeau (1998) argue that for
houses to have longer duration between
sales, they have to be older.
• Show that you can have heteroskedasticity
related BOTH to age and to time between
sales.
• CS method ALSO throws away LOTS of
data.
Modeling Heteroskedasticity
P   0    k zk   Age  
k
 i2   0  1 Age   2 Age2  3 Age3
or
|  i |  0  1 Age   2 Age2  3 Age3
Take reciprocal as weight, and re-estimate hedonic.
Iterate until convergence (usually 3 or 4 iterations)
Davidian, Marie, and Raymond J. Carroll. 1987. Variance
Function Estimation, J. Am. Stat. Ass’n 82 1079-1091.