HEDONIC ANALYSIS AS AN APPLICATION OF MULTIPLE REGRESSION

Austin 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 .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

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