HEDONIC ANALYSIS AS AN APPLICATION OF
MULTIPLE REGRESSION
Austin Troy
University of Vermont
Valuing bundled goods
 Being from France is not
directly priced, but by
comparing price of French
and non-French wines can
isolate that “premium.”
 The value of a 95+ mph split
finger fastball (SFF) is not
directly priced, but by
comparing the contract
trading price of a good SFF
pitcher against one without,
we can begin to price it
 Except….
Except…
 What if those two pitchers are not otherwise identical? (ie the
pitcher without the SFF happens to have several great
breaking pitches (e.g. slider), he’s a better batter, a little
older, and his ERA is a little lower
 Now, in order to see how the SFF affects the contract price,
we have to adjust for those other factors—hold them
constant.
 To make that comparison means we need enough pitchers to
analyze such that we have sufficient variation across all those
factors (a lot of other assumptions must be fulfilled, but we’ll
get into that later)
Now imagine a formula
 Price = function of:
1.
2.
3.
4.
5.
SFF (yes/no),
speed of SFF,
binary vector of other types of pitches (yes/no),
vector of average speeds for those pitches
Other stats (ERA, walks, strikes, age, etc.)
 If I get an equation that relates 1-5 against Price with
sufficient variability in the data set across attributes, I
can then “control” for 3-5, and get an estimate of how 1
and 2 contribute to price.
 That is, I “unbundled” the price of a major league pitcher
to price something that is not directly price in the market
Think of some other “bundled
Went a little
crazy with the
goods”
clip art
 Cars
 Food
 Computers
 Cell phones
 Hotel rooms
 Vacation packages
 REAL ESTATE
The housing bundle
 This “price unbundling” most commonly is
applied to real estate because
 It’s technically feasible:
 There are lots of housing transactions
 There are many easily quantifiable attributes
 There’s wide variation in housing attributes
 It’s important
 It’s the single most important asset class; is it being
valued correctly?
 Housing prices reflect so many non-market goods so
it’s a great way to value amenities and disamenities
Some parts of the housing
bundle that can be valued:








# bedrooms/bathrooms
Square footage
Attached garage
Age of house
Building material
Luxuries: pool, hot tub, 100 ft tall lawn gnome
Property taxes
Size of lot  Proxy for value of raw land
 However land value component can be further
broken down because it derives from location and…
…can also value things related
to location:
 “Quality” of neighborhood
 You’re buying piece of the neighborhood
 Often use proxies like income, crime, tenure, etc.
 Municipal services
 E.g. school district quality, availability of
sewer/water/trash service, etc.
 Site factors
 Soil/slope constraints, views, climate,
easements, hazards
 Proximity and accessibility to:
 Employment and services
 Transportation (transit, highways, etc.)
 Amenities and disamenities
Hedonic analysis
 Each component yields an “implicit” price, reflective
of WTP for a marginal change in a given attribute
 Price= fn(structure, neighborhood, location)
P    βS X S  β N X N  βLX L  e
 The result is a “schedule” of marginal prices for all
the elements of home value
 Can be used to create housing price indices
Linearity
 How does the relationship between price and
attributes vary with magnitude of x and y?
$18,000
$14,000
$12,000
$14,000
increas in price
increas in price
$16,000
$12,000
$10,000
$8,000
$6,000
$4,000
$2,000
$10,000
$8,000
$6,000
$4,000
$2,000
$-
1
2
3
4
5
6
7
8
number of rooms
9
10
11
$1
2
3
4
5
6
7
8
9
10
number of rooms
 One option is to transform independent
variables. Here we log transform # rooms
 So change in price now depends on number of
rooms at which price is evaluated
11
Functional form: dependent
variable transformation
 Linear model: 1 unit change in attribute results in 
change in price; however, linear model is unrealistic
 Semi-log model; take ln of price: interpret
coefficients as % changes in y due to 1 unit increase
in x; ie. Price effect depends on house price level at
which evaluated
 Log-log model: take ln of both sides: interpret
coefficients as elasticities; % change in y due to %
change in x; i.e. price effect depend both on level of
y and of x variables
 Box-Cox model: flexible functional form
 Uses a power transformation
 Ln, linear and sqrt are “special cases”
Hedonic assumptions:
 Single housing market:
 All variability in housing prices accounted for
 no omitted variable bias.
 Proper functional form
 No transaction costs
 Unlimited “repackaging” of attributes
 Independence of observations
 Exogeneity
 Price is dependent
Sample hedonic studies of open
space and forests
 Tyrvainen (1997): urban forests in




Joensuu, Finland—positive
Lutzenhizer and Netusil (2001)
and Bolitzer and Netusil (2000):
urban parks in Portland, OR—
positive
Netusil (2005): urban parks in
Portland OR—positive when the
park is more than 200 feet from
the property
Thompson, Hanna et al (2004):
urban interface tree health and
density in Tahoe Basin—positive
Nicholls and Crompton (2005):
linear greenways in Austin, TX—
positive effect when adjacent
Sample hedonic studies of open
space and forests
 Acharya and Bennett(2001): % of





open space up to 1 mile from a
house in CT—positive
Des Rosier (2002): proportion of
trees on property relative to
surroundings in Quebec City—
positive (scarcity effect)
Correll et al.(1978): greenbelts in
Boulder, CO—positive
Morancho (2003): park proximity
in Castellon; modest increase
Lacy (1990): open space in
subdivisions in MA—positive
Espey and Owusu-Edusei (2001):
urban parks in Greenville, SC—
negative
Example #1
A. Troy and J.M.
Grove. 2008.
Property Values,
parks, and crime:
a hedonic analysis
in Baltimore, MD.
Landscape and
Urban Planning.
87:233-245.
Methods
 Regress property price for ~25,000 property sales in
Baltimore against a range of control variables plus
amenity and crime variables
 4 models: 1) ln (d2 park); 2) lin (d2 park); 3) Box Cox trans
of price; 4) SAR model, ln (d2 park)
ln( P)    βC X C  β LC ln( X LC )   DP ln( X DP )   R X R   DPR ln( X DP ) X R  ei
XC
X LC
X DP
X R X DP
= vector of untransformed control variables
= vector of control variables to be log-transformed
= distance to park
= robbery rate for park area
ln( X DP ) X R =interaction term for previous two

=coefficient
Variables
MAIN EFFECTS:
 1999 and 2005 robbery rates
 Ln distance to nearest park (model 1);
distance to nearest park (model 2)
CONTROL VARIABLES:
 Ln square footage of structure
 Ln parcel area
 Ln improvement value (assessed)
 Bathrooms
 Years old
 Structure quality
 Single family home (1/0)
 Year transacted
 Whether house is renter occupied (1/0)
 Ln median HH income of BG
 % HS graduates in BG
 % owner occupied in BG
 Median age of BG
 Ln distance downtown
 Distance interstate
Models:
1. Log-log
2. Log-linear
3. Box-Cox
4. Spatial
Defining and attributing
parks
 “Parks” under 2 ha and
with less than 50%
vegetated surface
were removed to get
rid of things like
highway buffers,
median strips, paved
pocket parks and other
park “fragments” with
low amenity value
Data acquisition: parks
Data acquisition: parks
Term
Model 1
Model 2
Sig.
PARC.AREA
+
+
**/**
Ln(SQFTSTRC)
+
+
**/**
YEAROLD
+
+
**/**
YEAROLD2
+
+
**/**
BATHS
+
+
**/**
ln(MED.HH.INC)
+
+
**/**
P.OWNOCC
-
-
**/**
X2001
-
-
**/**
X2002
-
-
**/**
X2003
-
-
*/*
P.HS
+
+
**/**
MED.AGE
+
+
**/**
RENTEROCC
-
-
**/**
Ln(DWTWN.DIST)
-
-
**/**
Ln(INSTE.DIST)
-
-
**/**
STRU.MED
+
+
**/**
STRU.HIGH
+
+
**/**
SFH
+
+
**/**
ln(distance to park)/ Distance to
park
-0.022
-0.00005
**/**
-0.000433
-0.00017
**/**
0.000054
0.00000011
**/**
Robbery/rape rate
ln(distance to park):robbery
Results
R-squared of .66
Relatively low fit relates to
problems with central city
property data
All control variables
significant with expected
sign
Main effects are expected
sign and significance
Interaction is significant
Almost no difference when
using 1999 vs 2005 crime
data
Results: park & crime
interaction
 For lower crime levels,
price increases with
proximity to park, all
else constant.
 As crime rate increases,
curve gets less steep
 At a certain crime level,
(~450% of national
average) the curve
reverses direction
 Mean 2005 robbery
index is 475% of
national average for
Baltimore
Results: tree percentage
 Above ~450%
crime levels,
property price
decreases with
proximity to parks
 Gets steeper as
crime rate
increases
 At mean crime
rate for city
(475%), parks are
valued negatively!
Model 2: linear versions
Result basically the same, but get lines instead of asymptotic curves
Classifying parks
Hypothetical price effects