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Austin Troy University of Vermont. HEDONIC ANALYSIS AS AN APPLICATION OF MULTIPLE REGRESSION. Valuing bundled goods. Being from France is not directly priced, but by comparing price of French and non-French wines can isolate that “premium.” - PowerPoint PPT Presentation
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HEDONIC ANALYSIS AS AN APPLICATION OF MULTIPLE REGRESSIONAustin TroyUniversity 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. SFF (yes/no), 2. speed of SFF, 3. binary vector of other types of pitches (yes/no),4. vector of average speeds for those pitches5. 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 goods” Cars Food Computers Cell phones Hotel rooms Vacation packages REAL ESTATE
Went a little crazy with the clip art
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)
The result is a “schedule” of marginal prices for all the elements of home value
Can be used to create housing price indices
eP LLNNSS XβXβXβ
Linearity How does the relationship between price and
attributes vary with magnitude of x and y?
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
1 2 3 4 5 6 7 8 9 10 11 $- $2,000 $4,000 $6,000 $8,000
$10,000 $12,000 $14,000 $16,000 $18,000
number of rooms
incr
eas
in p
rice
1 2 3 4 5 6 7 8 9 10 11 $-
$2,000
$4,000
$6,000
$8,000
$10,000
$12,000
$14,000
number of rooms
incr
eas
in p
rice
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)
RDP XX )ln(
= vector of untransformed control variables
= vector of control variables to be log-transformed
= distance to park
= robbery rate for park area
=interaction term for previous two
=coefficient
CXiRDPDPRRRDPDPLCLCCC eXXXXP )ln()ln()ln()ln( XβXβ
DPRXX
LCX
DPX
VariablesMAIN 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-log2. Log-linear3. Box-Cox4. 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 **/**
Robbery/rape rate -0.000433 -0.00017 **/**
ln(distance to park):robbery 0.000054 0.00000011 **/**
R-squared of .66Relatively low fit relates to problems with central city property dataAll control variables significant with expected signMain effects are expected sign and significanceInteraction is significantAlmost no difference when using 1999 vs 2005 crime data
Results
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 versionsResult basically the same, but get lines instead of asymptotic curves
Classifying parks
Hypothetical price effects