Environmental Valuation using Revealed

Preference Methods

• Lectures include:– A little welfare economic

theory that forms basis of environmental valuation techniques

– Conceptual implementation issues

– Econometric implementation issues

• Illustrations using actual applications

• Hands-on experience using actual data

Why are there so many more stated preference

than revealed preference studies?

• Less statistical knowledge necessary? (perhaps?)

• RP can’t handle existence value? (not always relevant)

• Nature conspires against revealed preference methods

What Concepts Do We Need?

• A theoretical model of how people make decisions in some environmentally related context

• A means of relating this behavior to a well-defined welfare measure

• A means of obtaining consistent estimates of the parameters of the behavioral functions

• A mathematical relationship between the parameters and the welfare measure

What Data/Circumstances Do We Need for RP

Methods to have a Chance?

• Behavior “footprints” – environmental change must influence some behavior

• Behavioral change must constitute most of, and not more than, a response to environmental change

• Behavior must relate to money prices

Stated and Revealed Preference

• Stated preference methods– very sensitive to way ask question– not so sensitive to econometric

specification

• Revealed preference – not so sensitive to data collection

methods – very sensitive to econometric

specification

Why?

• In SP you are asking people directly for their values

• In RP you are asking people for facts and then you are deducing values based on models of behavior

Types of Environmental Amenities/Goods that Are

Often Valued Using Revealed Preference

• Natural, preserved sites (e.g. parks, nature-based recreational areas)

• Environmental quality or amenities at these sites

• Ambient environmental quality/risks (at the individual’s residential location)

• Environmental quality/risks at individual’s work-site

• Environmental inputs into production

Empirical Models• Natural sites

– Single site demand models– Random utility models

• Site environmental quality– Systems of demand functions– Random utility models

• Ambient environmental quality– Hedonic models– Averting behavior models– Random utility models

• Job-related environmental qual.– Hedonic models– Averting behavior models– Random utility models

• Inputs into production– Supply/demand functions– Random utility models

Theoretical Restrictions and Models

• The environment as an input into production– Household production– Firm’s profit maximization (sometimes

under risk and uncertainty)

• The environment as a “weak complement” to privately consumed goods:– Household production models of single

goods– Random utility models of choice

• The environment as a quality characteristic of a marketed good – – hedonic models

Cases we will look at in this course

Valuing:• Existence of a site using a

single site recreation demand model

• Environmental amenity using a random utility model

• Environmental good as an input into fisheries production using a random utility model

[ Environmental quality as a characteristic of a marketed good – Dr. Tyrvainen ]

Theoretical Underpinnings of

Welfare Economics

Notation – the utility maximization problem

Individual is assumed to:

Max U(q) + (y - pq)where

U=utility

q=vector of privately consumed goods

p=corresponding vector of prices

y=income

=LaGrangian multiplier

Notation – important functions in welfare

economics

Indirect utility function:

v(p,y) = U(q) + (y - pq)

Expenditure function:

m(p,U) =min pq+ (U0-U(q))

Conventional measures of benefits and losses (applied

“welfare” measures)

Compensating variation (CV) =

amount of money necessary to “compensate” for an exogenous change in circumstances

Then CV of change is defined implicitly as:

v(p10,p-1

0,y)=v(p11,p-1

0,y-CV)

Suppose a price changes, p10 p1

1

CV is signed here according to the direction of the welfare change.

Compensating variation in terms of expenditure

function

CV is an explicit function in terms of expenditure function:

11

011

001

11

01

),,(),,(

dpp

m

UpmUpmCVp

p

01

01 pp

Importance of Shepherd’s Lemma in Standard Welfare Analysis

Partial derivative of m equals compensated demand:

1111

11

01

11

01

dpqdpp

mCV

p

p

hp

p

p10

p11

q10 q1

1

Compensated demand function

CV measure

Price

Quantity

Usually observe Marshallian demands, but..

Results that relate the consumer surplus (CS) and compensating variation (CV):

• If income effects are negligible, then CS = CV

• Can bound CV by a function of income elasticities and CS (Willig)

• Can integrate back from Marshallian function to expenditure function

Valuing a change in an environmental good

Suppose “b” is our environmental amenity. If individuals care about b for whatever reason, it will show up in the expenditure function.

CV measure for a change in b is:

CV = m(p0,b0,U0)-m(p0,b1,U0)

How can we get an approximation of this?

• From this point on there is no general theory. There is no analog to Shepherd’s lemma for environmental quality changes.

is typically not a behavior function

• There are only strategies that: – may or may not be applicable

(depending on nature of behavior)

– may or may not be feasible

(depending on availability of data)

bm

Valuing the Existence of a (Natural) Site

If b denotes the site, in the sense that b=1 means the site exists, then the individual’s general model is:

Max U(q,b) + (y-pq)

But unless there is some further restrictions on this problem, there is no hope of using RP to value b.

A simple way to frame the problem:

The individual only cares about the existence of the site if he visits the site (weak complementarity).

The individual derives utility from visiting the site.

A demand curve for site visits can be constructed using access costs as price.

Elimination of the site is equivalent to pricing access high enough so no trips are taken.

Could Cast in Household Production

Framework max U(q,z(b,x))+(y-pq-rx)

where

q=other goods

z=household produced good (trips to site)

b=index of site’s existence

x=other inputs into

production of trips to site

r=input prices

Welfare measure is “simple”

Treat as a “price” change from existing price (marginal cost)

to “choke” price.constant marginalcost of producing z

quantity ofvisits

zc~

0zc

z0

CV (or CS) measure of value of site

Implicit demand function for household produced z

Issues of Implementation

• Specification Issues:– Time Allocation– Substitution

• Estimation Issues:– Censored Samples– Truncated Samples

Specification Issue #1: Value of Time

Models of recreational demand are really household production models.

Household production models are about allocating both money and time.

Household Production Including Time Allocation

Maximization decision is now:

)()''(

)),,(,(max,,

thTxrqpwhm

btxzqUqtx

The household production function now includes time spent in taking trips.The money constraint explicitly takes account of labor time.

Valuing time as function of wage rate

If people can easily substitute work for leisure, then the opportunity cost of time is (after-tax) wages and two constraints collapse into one:

)''(

)),,(,(max

)'')((

)),,(,(max

,,

,,

wtxrqpwTm

btxzqU

xrqptTwm

btxzqU

qtx

qtx

Full incomeFull price

Corner and Interior Solutions in Labor Market

If some people have fixed work times, then work/leisure substitution may not be easy.

In these cases, time constraint does not collapse into money constraint and two constraints remain.

Some Labor Market Solutions

Leisure

Money

T=total available time

Slope=wage rate

h=labor

Earned income =w*h

indifference curve

T=total available timeLeisure

Money

Earned income =w*h

Slope=implicit wage rate of primary job

INTERIORSOLUTION

CORNERSOLUTION

h=labor

Slope=wage rate of secondary job

In Practice….

• Labor market model has better theoretical basis, but…– Difficult to determine which

respondents have flexible time– Sometimes multicollinearity

between time and money costs if included separately in model

• “Ad hoc” opportunity cost of time model often values time at some fraction of the wage rate (e.g. .4 or .5 – may change with different tax rates)

What happens if ignore time costs?

Since time costs and money costs are generally correlated, leaving out time will cause an upward bias in the coefficient on money costs.

“True” model is:

...)(

)(

2

10

wTwhm

wtcz

But you estimate:

...)(2

10

whm

cz

If measuring value of site…

with a linear demand function…

Number of tripsz

“true” 1/1

biased 1/1 estimate

Constant marginalcost of z

Consumer surplus =1

2

2z

0zc

(Note: since the dependent variable in the model is trips, the slope of the line in the graph is really 1/1).

Consumer surplus is underestimated

If measuring value of site…

with a semi-log demand function,

consumer surplus = -z/1

Estimate of CS will also be biased downward if your estimate of 1 is biased upward.

Specification issue #2:

Demand function for z should include money and time costs (and environmental quality) of substitutes.

If substitutes left out and these are correlated over the sample with the “own” money and time costs (and quality), then estimates will be biased.

Suppose there are two sites, A and B, thatare substitutes in recreation.

As you look across observations on people who visit these sites, suppose people who live far from one site also tend to live relatively far from the other site.

Now, suppose you make the mistake of estimating the demand for trips to site A without including costs to site B.

Trips to site A

Cost of accessingsite A

Biased estimate

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),( 11BAA ccz

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Washington, DC

Baltimore, MD

Beach Areas

Population density:Blue – highestYellow - lowest