18. Hedonic Price Analysis

Kolstad, Ch. 8 (IV)

Hanley and Barbier, Ch 5

1. Intuition and Stories Revealed preference studies using

housing (or land markets) and labor marketsSimple hedonics story w/ 2 houses

• Assume houses are identical in every respect except that B is located in a polluted area

• If they sell for the same price, everyone buys A

Air pollution

A B

• Say B is offered at some discount (to entice buyers)A $100,000B $ 95,000

• Now, individuals implicitly face the decision: Is the clean air worth $5,000?If yes, buy AIf no, buy B

• Individuals reveal something about the value (wtp) of clean air in the market decision.

How would markets clear in a simple case like this?

• Imagine many A’s and B’s

• Imagine all houses start at $100,000Excess demand for A Prices riseExcess supply for B Prices fall

• Gap opens up and continues to widen until individuals are sufficiently compensated by price drop to live in polluted area. Settle into an equilibrium in the housing market

A B$105,000 $75,000

Implicit value of clean air is $30,000/house. We call thisa “hedonic” or “implicit” price.

• Commentsopen mkt and governing the priceidentical people and perfect compensationrent vs. asset value

Value for environmental quality “revealed” in housing or property values and based on individual preferences (and supply). More important air quality is the high the hedonic price will be.

Real housing (land) markets are not so simple. Housing choice and price depends on many characteristics: structural, neighborhood, and locational.• Each has an implicit value• Hedonic price technique is a method for

sorting out these valuesThink about the $30,000 being due to more than just

pollution.Works for any differentiated product: cars, food, comic

books

Environmental Goods in Land Markets• Air pollution (37 studies)

• Landfill/Hazardous waste sites

• Proximity to open space

• Crop damage/Agricultural

• Airport noise

“Capitalized” values• Crime

• Frat House

Price

Distance to the waste site

2. The Mechanics of the Hedonic Price Method (Property Values)

• Postulate a functional relationship between housing prices and characteristics of houses:

( , , )P f s n e

Vector of Structural Attributes:# RoomsLot sizeAgeBasement (yes/no)Design and so on Vector of Neighborhood Attributes:

School qualityOpen spaceDistance from downtownDistance form shopping and so on

Vector of Environmental Attributes:Air qualityDistance to waste siteNoise levels and so on

Hedonic price function

• You may set this up in a linear or nonlinear way. Here is a typical linear form:

• Focus on the parameter . It tells us the relationship between Price and Air Quality.Take the first derivative of f(.) with respect to AirQ and

you get

1 2 3 4

- + - + Age LotSize DistCBDP AirQ

Coefficients tell us the relationship between each characteristic and housing prices. Note expected signsabove the coefficients.

4

4

P

AirQ

Implicit Price of a Unitof Air Quality in the Housing Market

• So, we set out to estimate the coefficients in the Hedonic Price Function. To do this we need data on housing sales: price and characteristics of houses sold in the market. Data set looks something like this

• House Price Age Lot Size Air Quality and so on ………………… .

(Dollars) (Years) (Acres) (Visibility Days)

1 $85,000 17 0.5 101

2 65,000 2 0.25 23

3 211,000 5 1 4

4 92,000 22 0.33 5

5 300,000 1 1.5 1

.

.

.

100 202,500 2 0.66 14

More characteristics

Number of observations

• Regress House Price on characteristics and this gives estimates of the parameters in

• Focus on AirQ for an estimate of the implicit value of air quality.

• Theory

This is the implicit price function for characteristic#1, holding all other characteristics fixed. Note: need not be flat!

1

P

z

1zmv

*1z

3. Some Theory• House Mkt Equilibrium gives P(z).

• Individuals take P(z) as fixed.

• Individuals choose z and x (composite good) to maximize utility

1 2

1 2

( , ,....., , )

. . ( , ,....., )

n

n

Max U z z z x

s t I x P z z z

Note that the individual is choosing attributes

( , ) / ( ) (i) for all

( , ) / (ii)

i

1

i

i

foc

U z x z P z

z

U z x x

iMarginal value of z

iImplicit price of z

is a vector of housing characteristics, like , , in our earlier examplez

s n e

• Shopping chart analogy, “implicit” decision

• Graphically

This is the implicit price function for characteristic#1, holding all other characteristics fixed. Note: need not be flat!

1

P

z

1zmv

*1z

n

P

z

nzmv

*nz

There is a similar graph for each characteristic. It is as though the person is choosing n separate goods.

• Different people w/ different income and taste will consume different levels of each characteristic

• You end-up with different people at different points on the implicit price line.

• What if the population is homogeneous?

8

P

z

8

1zmv

1*8z

8

2zmv

2*8z

Person #1Person #2

5. IssuesFunctional form

• Probably not linear, so often estimated as a nonlinear function

( , )P AirQ z

AirQ

( )P z

( , )P AirQ z

AirQ

( )P z

4

4

..... ln( ) .....

(.)

P AirQ

P

AirQ AirQ

One nonlinear case

• Flexible forms (Box-Cox)

Measurement of quality variables• Air pollution

TSP,SO2Visibility indexesClear days

• LandfillDistance

• Views

• Crime Levels

• Noise

Colinearity• Disamenities and amenities “run” together

Discreteness, lumpy bundles

Perception• Health vs. Visibility

Market segmentation• 2 or more housing mkts

*1z

1( )P z2( )P z

Market disequilibriumIncomplete benefit assessment

• nonuse

• other non-resident benefits

The identification problem

• We estimate the blue line (the implicit price function) when we estimate the hendonic price function.

• But, we can not in a single housing mkt estimate the individual marginal value (MV) functions. These are the demand curves for the attributes.

1

P

z

1

2zmv

1

3zmv

1*1z 2*

1z3*1z

1

1zmv

• Because we only observe each individual at one point on his or her demand curve, we can not determine the shape of the entire demand curve.

• Everyone the same, again.

• Implicationsreally only have marginal values for each personforced to use hedonic to approximate non-marginal

changesneed multi-market data to identify marginal value’s (at

least this is the major way to fix the problem) See next slide.

•

1

( 1)P

mktz

1

2zmv

1

3zmv

1*1z 2*

1z3*1z

1

( 2)P

mktz

1

1zmv

Now we can begin to get at the shapes (“identify”) of the mv functions,and begin to think about consumer surplus w/ hedonics.

Repeat sale analysis• Having data on the same houses before and after an

episode of some sort. New landfill, airport ….

• Controlling for other factors difficult

(.)beforeP

(.)afterP

Wages and Land interacting

C.A.Kolstad, Environmental Economics,Oxford U. Press, 2000. C.A.Kolstad, Environmental Economics,

Oxford U. Press, 2000.

Pollution is productive Pollution is not productive

5. Valuation/Consumer SurplusMarginal changes

• Use marginal values from the hedonic

Non-marginal changes• Short-run

1

P

z

1zmv

A

B

01z

11z Consider an increase in quality

(as a housing attribute)Area A is the short run benefitsof the improvement. Discuss.

Since mv is difficult to measure, often useArea A+B as an upperbound.

What if z declines?

• Long runGets complicated because hedonic shifts and people moveConsider this shift from a clean-up

1

P

z

1z

mv

2

P

z

01z

1afterz

1before movez

Special cases• Small mkt

• Identical individuals

6. Wage Hedonics and the Value of LifeThe Basics

• Same basic analysis w/ job mkt data

• Interested in valuing small reductions in risk of death

• Many regs are concerned w/ health and associated risk reductionair pollutionhazardous waste removaltransportation safetyhealth care initatives

• Hedonic wages studies are one way to infer value for risk of death

• Intuition and StoryScaffolding storyWage compensating differentialDynamics

( , , , )jc wcWage rdRate f ri

Vector of Job Characteristics:Union (yes/no)SkilledManagementLocation and so on

Vector of worker characteristics:AgeExperienceEducation and so on

Risk of Death

Risk of Injury

Wage Hedonic

• Specify functional form and focus on parameter on the rd variable

• Many of the same issues here as in property value studiescollinearityidentification

Statistical Lives • Common Parlance

• Definition (by example)Population 100,000Risk of Death per Person .003In this case we say 300 statistical lives will be lost.

» 100,000 * .003 = 300We say that these are not “identified” lives

• Assume we can reduce risks by introducing some regulations. Say risks drop from .003 to .002.After the regulation, 200 statistical lives are lost in the

populationWe say that the regulation saved 100 statistical lives

• Assume in a top notch wage hedonic study that we discover individuals are willing to pay $500 (revealed in the job market) for a reduction of .001.

• If so, in a population of 1,000 people, one statistical life will be saved. Each of the 1,000 persons has an ex ante value for risk reduction .001 of $500.

Ex antereally value risk reduction

$500,000 is the Value of a Statistical Life

• EPA, OSHA, and so on

• Cost per life saved studies and use of value of life estimates

• IssuesVoluntaryIllness and quality of life