Download Environmental Valuation using Revealed Preference Methods

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 - pq)
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 - pq)
Expenditure function:
m(p,U) =min pq+ (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
Suppose a price changes, p10 p11
Then CV of change is defined
implicitly as:
v(p10,p-10,y)=v(p11,p-10,y-CV)
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:
CV  m( p , p ,U )  m( p , p ,U )
0
1
m
0
dp1
p1 p
1
p11
0
1
0
1
1
0
1
0
Importance of Shepherd’s
Lemma in Standard
Welfare Analysis
Partial derivative of m equals
compensated demand:
p11
m
CV   0
dp1   0 q1h dp1
p1 p
p1
1
p11
Price
CV measure
p10
p11
Compensated
demand function
q10
q11
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.
m
b
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)
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-pq)
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-pq-rx)
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 marginal
cost of producing z
c~z
CV (or CS) measure of
value of site
cz0
Implicit demand function
for household produced z
z0
quantity of
visits
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 U ( q, z ( x, t ), b)
x ,t , q
  (m  wh  p' q  r ' x )   (T  h  t )
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 U ( q, z ( x, t ), b) 
x ,t , q
 (m  w(T  t )  p' q  r ' x ) 
max U ( q, z ( x, t ), b) 
x ,t , q
 (m  wT  p' q  r ' x  wt )
Full income
Full 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
Money
Earned income
=w*h
indifference curve
INTERIOR
SOLUTION
Slope=wage rate
Leisure
T=total available time
h=labor
Money
CORNER
SOLUTION
Slope=wage rate of secondary job
Earned income
=w*h
Slope=implicit wage rate
of primary job
Leisure
h=labor
T=total available time
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:
z  0  1 (c  wt)
  2 (m  wh  wT )  ...
But you estimate:
z   0  1c
  2 (m  wh)  ...
If measuring value of site…
with a linear demand function…
Constant marginal
cost of z
“true” 1/1
biased 1/1 estimate
cz0
z
Number of trips
(Note: since the dependent variable in the
model is trips, the slope of the line in the graph
is really 1/1).
Consumer surplus =
 z2
2 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, that
are 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.
Cost of
accessing
site A
Biased estimate
z A   0   Ac A   B c1B
c1A
c
z A   0   Ac A   B cB0
0
A
z A (c1A , c1B )
z A (c 0A , cB0 )
Trips to site A
Baltimore, MD
Washington, DC
Beach
Areas
Population density:
Blue – highest
Yellow - lowest