Valuation 9:
Travel cost model
• A simple travel cost model of a single site
• Multiple sites
• Implementation
– The zonal travel cost method
– The individual travel cost model
• Travel cost with a random utility model
Last week
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Revealed preference methods
Defensive expenditures
Damage costs
Defensive expenditures: A simple
model
• An example: Urban ozone
Travel cost model
• Most frequently applied to valuation of natural
environments that people visit to appreciate
– Recreation loss due to closure of a site
– Recreation gain associated with improved quality
• Natural areas seldom command a price in the
market
• Basic premise: time and travel cost expenses
represent the „price“ of access to the site
– WTP to visit the site
• Travel is a complement to recreation
Travel cost model – 2
• Application of TCM
– Reservoir management, water supply, wildlife,
forests, outdoor recreation etc.
• History: Harold Hotelling 1947
– Value of national parks
• Variations of the method
– Simple zonal travel cost approach
– Individual travel cost approach
– Random utility approach
A simple model of a single site
• A single consumer and a single site
• The park has the quality q
– higher qs are better
• Consumer chooses between visit to the park (v)
and market goods (x)
• He works for L hours at a wage w and has a total
budget of time T
• He spends p0 for the single trip
• The maximisation problem is: maxU (x ,v , q )
x ,v
s.t. wL  x  p0v
and T  L  (tt  tv )v
A simple model (2)
• The maximisation problem is:
maxU (x ,v , q )
x ,v
s.t. wL  x  p0v and T  L  (tt  tv )v
• The maximisation problem can be reduced to
maxU (x ,v , q )
x ,v
s.t. wT  x  pvv where pv  p0  w (tt  tv )
• For a particular consumer the demand function
for visits to the park is:
v  f ( pv , q , y )
Quality changes
• What is the WTP for a small increase in quality?
– For a given price the demand increases
– Consumer would visit more often
• What is the marginal WTP ?
– Surplus gain from quality increase / change in quality
pv
A
p*
C
B
f(pv,q1+Dq,y)
f(pv,q1,y)
v1
v2
v
Multiple sites
• If we repeat the above experiment for a variety
of quality levels, the marginal WTP-function for
quality can be generated
• However, consumer chooses among multiple sites
• The demand for one site is a function of the
prices of the other sites as well as the qualities
• For three sites the demand function for one site
changes to
vA  fA ( pA , pB , pC , qA , qB , qC , y )
• This is straightforward but empirical application is
more complicated
• Random utility models (RUM)
Multiple sites - 2
• Visiting site i gives utility u i =f(b , p,i q i, y) + ei
• b is a parameter and e is an error term
representing unknown factors
• We do not observe utility but consumer choice
• If consumer chooses site i over site j than ui > uj
• Different values of b yield in different values of ui
and uj
• From b we can compute the demand for trips to a
site as a function of quality of the site and the
price of a visit
• We can then examine how demand changes when
quality of the site changes
Implementation:
Zonal travel cost approach
• The approach follows directly from the original
suggestion of Hotelling
• Gives values of the site as a whole
– The elimination of a site would be a typical application
• It is also possible to value the change associated
with a change in the cost of access to a site
• Based on number of visits from different
distances
– Travel and time costs increase with distance
– Gives information on „quantities“ and „prices“
– Construct a demand function of the site
Steps
• Define a set of zones surrounding the site
• Collect number of visitors from each zone
in a certain period
• Calculate visitation rates per population
• Calculate round-trip distance and travel
time
• Estimate visitors per period and derive
demand function
An example
Zone Visits/Year Population Visits/1000 Total travel
costs
0
400
1000
400
0
1
400
2000
200
10.5
2
400
4000
100
21.0
3
400
8000
50
42.0
Visits/1000 = 300 – 7.755 * Travel Costs
An entrance fee of 10 Euro
Zone Costs
Visits/1000 Population Visits
0
10.0
222
1000
222
1
20.5
141
2000
282
2
31.0
60
4000
240
3
52.0
0
8000
0
Total
744
So now we have two points on our demand curve.
Demand Curve
45
Additional Costs/Trip
40
0
35
30
67
25
20
272
15
10
744
5
1600
0
Total Visitors
Drawbacks
• Not data intensive, but a number of
shortcomings
• Assumes that all residents in a zone
are the same
• Individual data might be used instead
• More expensive
• Sample selection bias, only visitors
are included
Other problems
• Assumption that people respond to changes
in travel costs the same way they would
respond to changes in admission price
• Opportunity cost of time
• Single purpose trip
• Substitute sites
• Unable to look at most interesting policy
questions: changes in quality
Implementation:
Individual travel cost approach
• Single-site application of beach recreation on Lake Erie
within two parks in 1997 (Sohngen, 2000)
– Maumee Bay State Park (Western Ohio) offers opportunities
beyond beach use
– Headlands State Park (Eastern Ohio) is more natural
• Data is gathered on-site (returned by mail)
– Single-day visits by people living within 150 miles of the site
– Response rate was 52% (394) for Headlands and 62% (376) for
Maumee Bay
• Substitute sites
– Nearby beaches similar in character
– One substitute site for Maumee Bay and two for Headlands
Model specification
• Variables included
–
–
–
–
Own price
Substitute prices
Income
Importance (scale from 1 to 5) of water quality, maintenance,
cleanliness, congestion and facilities
– Dummy variable measures whether or not the primary purpose
of the trip was beach use
• Trip cost was measured as the sum of travel expenses and
time cost
– Time cost: imputed wages (30% of hourly wage) times travel
time
• Functional form
– They tried different specifications and chose a Poisson
regression
The results
• Per-person-per-trip
values are:
• $25 for Maumee Bay
=1/0.04
• $38 for Headlands
=1/0.026
Parameter Estimates
Variables
tcr
Income
Maumee Bay
-0.040 ***
Headlands
-0.026 ***
0.018
0.040 ***
Sole
-0.018
0.292 ***
tcs1
0.004 ***
0.005
tcs2
-0.004
Water quality
-0.053
-0.139 ***
Maintenance
-0.270 ***
0.033
0.176 **
0.028
Cleanliness
Congestion
-0.065 *
Facilities
0.098 **
Constant
2.648 ***
-0.066 ***
-0.004
2.433 ***
R2
0.38
0.29
Sample Size
230
345
Random utility models
• Extremely flexible and account for
individuals ability to substitute between
sites
• Can estimate welfare changes associated
with:
– Quality changes at one/many sites
– Loss of one/many sites
– Creation of one/many new sites
• Main drawback: estimate welfare changes
associated with each trip
– Visitors might change their number of visits
Sum up: Alternative TCMs
• Zonal travel cost method – trips to
one site by classes of people
• Individual travel cost method – trips
to one site by individual people
• Random utility models – trips to
multiple sites by individual people