Valuation 8: Defensive
expenditures (HPF)
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Revealed preference methods
Defensive expenditures
Damage costs
Defensive expenditures: A simple
model
• An example: Urban ozone
Last week
• Contingent choice modelling and its
variants
• Steps and design stages for choice
modelling
• Some econometrics
• Application to green product choice
Revealed preference
methods
• People make choices within markets: prices
paid and quantities purchased
• Derive values people place on environmental
amenities and disamenities from purchase
decisions
• Stated preference methods: intended
behaviour; non-use values
• Four commonly used methods: TCM, HPM,
defensive expenditures and damage costs
Revealed preference methods -2
Method
Revealed
Behaviour
Conceptual
Framework
Hedonic
Property
purchased or
choice of
employment
Demand for
Property value
differentiated and wage
goods
models
Travel Cost
Participation in
recreation
activity and site
chosen
HPF, weak
complements
Recreation
demand
Defensive
Expenditures to
Expenditures avoid illness or
death
HPF, mostly
substitutes
Morbidity
/mortality
Cost of
Illness
Treatment
costs
Morbidity
Expenditures to
treat illness
Types of
Application
The Household production function
approach
• A household combines an environmental good/bad
with market goods to produce and „experience“
that directly provides utility
• To enjoy a national park people must visit the park
and this costs money
• To defend against an environmental bad such as
traffic noise money is spent on insulation
• The household production function (HPF) approach
involves investigating changes in the consumption
of commodities that are substitutes or
complements for the environmental good of
interest
Defensive expenditures
• Measures the “demand” for environmental bads
• A rational consumer buys self-protection up to the
point where the marginal cost of additional
measures exceeds the marginal benefits from the
reduction
• Averting inputs include air filters, water purifiers,
noise insulation and other defensive or selfprotection inputs; these are substitutes
• In all these cases an individual combines quantities
of a public bad with a quantity of a market good to
produce what actually gives utility
Excurse: Damage costs
• The method estimates the resource cost
associated with environmental change, rather than
WTP
– Does not include any estimate of consumer surplus or
marginal prices
• In the health context: cost of illness approach
• This is the sum of direct and indirect costs
associated with illness, injury, or death
• Direct costs (out-of pocket expenses)
– Diagnose, treat, rehabilitate, or support ill or injured
persons
• Indirect costs (the value of output that is not
produced)
– Mainly foregone earnings
Defensive expenditure:
A simple model
• Noise pollution (P) from a nearby road
– higher Ps are worse
• The individual is only interested in the level of
quiet within the house (Q)
– higher Q is better
• The homeowner buys noise insulation and other
equipment to reduce the level of noise within the
house
• Defensive expenditure: D(Q,P) to achieve Q for a
given P
The homeowner’s problem
• The homeowner’s problem to choose between conventional
goods (X) and Q is:
maxU (X ,Q ) s.t. X  D (Q , P )  Y
X ,Q
• Outdoor noise does not enter the utility function, it is
outside of the control of the individual
X
D(Q*,P)
Y
X*
U1=U(X,Q)
U0=U(X,Q)
Y=X+D(Q,P)
Q*
Q
A simple model (2)
• Suppose the level of noise (P) increases
slightly
– consumer has to spend more to achieve same
noise level
• If income increases
– The level of utility is the same
– Compensating surplus
• What happens if income is not adjusted?
– Lower level of utility
– Substitution effects: Q drops
• Defensive expenditure < true marginal WTP
The effect of a change in pollution
X
P2 > P1
Y=X+D(Q,P2)
Y=X+D(Q,P1)
U1
U2
Q2*
Q1*
Q
Algebraically
• Suppose we change P slightly by DP
• The consumer adjusts the choice of Q and X
• Defensive expenditure changes by DD and indoor noise levels
by DQ
DD=D(Q+DQ, P + DP)-D(Q,P)
=D(Q+DQ, P + DP)-D(Q, P + DP)+ D(Q, P + DP)-D(Q,P)
=DQDQ+DPDP
DQ=[D(Q+DQ, P + DP)-D(Q, P + DP)]/ DQ
DP=[D(Q, P + DP)-D(Q,P)]/ DP
The marginal WTP to avoid a change in P
DD/DP =DQ(DQ/DP)+DP
Generally: DD/DP <DP
An example: Urban ozone
• Significant extension to previous model
– pollution level enters directly into the utility function
• Study by Dickie and Gerking (1991)
• Estimate the demand for ozone pollution for two
cities in the metropolitan area of Los Angeles
– Burbank and Glendora
• Compare the results to out-of-pocket medical
expenses (damage costs) associated with elevated
ozone in each of the two cities
Burbank and Glendora
Number of days
• 80Suppose
Burbank
60
Glendora
40
New
Standard
Old
Standard
20
0
1.5
5
8
11
14
15
20
Daily ozone peak (pphm)
23
26
28
The basis of the analysis
• Both cities have a significant amount of air
pollution
• What is the WTP for an average resident of each
city to reduce the maximum ozone level during a
year to either 12 or 9 pphm?
• The analysis is based on people’s willingness to
purchase health care to compensate for the
health-related damage from ozone pollution
• Ozone causes coughing and other breathing
difficulties
The modelling approach
• Utility is a function of market goods (X), health (H) and
exposure to air pollution (A)
maxU (X , H , A )
X ,M
s.t. H  h (M , R , A )
and wT  qx X  qM M  wG (H )
• Defensive expenditure (M) depends on health (H), air
pollution (A) and the individuals health status (R)
• We write this as a health production function which tells us
how much health will result if M is spent on medical care
• The budget constraint is defined on the basis of time
available to generate income
The modelling approach (2)
• The indirect utility function giving maximum utility
attainable is
v V (w , qx , qM , R , A)
• If we could observe utility we could statistically estimate
the equation
• Dickie and Gerking compensate this by observing whether
people visit a doctor
• If they do, there must be a utility gain from visiting
and V1 (M>0) > V0 (M=0)
• They use a random probability model and estimate the
probability to visit a doctor
• The binary choice problem is
M>0 if V1 - V0 > 0 and M=0 if V1 - V0 = 0
The data
• Sample of 256 residents of the two cities
• All are household heads with full-time jobs
• Married white males with compromised respiratory
functions are oversampled
• Respondents were asked about
– long-term health status
– contacts with the medical care delivery system
– socio-economic/demographic and work environmental
characteristics
– typical out-of-pocket expenses incurred for a visit to
their doctor
– commuting and waiting time required to see their doctor
• Each contact with a respondent was matched to
daily measures of ambient air pollution
concentrations
The results
Conclusion
• Estimates are lower bounds
• As expected, out-of-pocket medical expenses are
much lower
• Earlier studies on defensive expenditures found
much smaller values
–
–
–
–
$0.04 to $4.00 per year per person
Other regions
Lower ozone levels
No oversampling of respiratory impaired
• CV studies found similar values
• The broad range of WTP estimates poses an
awkward situation for policy makers