1. 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

2. Last week Revealed preference methods Defensive expenditures
Damage costs
Defensive expenditures: A simple model
An example: Urban ozone

3. 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

4. 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

5. 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:

6. A simple model (2) The maximisation problem is:
The maximisation problem can be reduced to
For a particular consumer the demand function for visits to the park is:

7. 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 C p* B
f(pv,q1+Dq,y)
f(pv,q1,y) v1 v2 v

8. 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
This is straightforward but empirical application is more complicated
Random utility models (RUM)

9. Multiple sites - 2 Visiting site i gives utility
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

10. 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

11. 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

12. An example Visits/1000 = 300 – 7.755 * Travel Costs Zone Visits/Year
Population
Visits/1000
Total travel costs
400
1000 1
2000
200
10.5 2
4000
100
21.0 3
8000 50
42.0
Visits/1000 = 300 – * Travel Costs

13. An entrance fee of 10 Euro Zone Costs Visits/1000 Population Visits
10.0
222
1000 1
20.5
141
2000
282 2
31.0 60
4000
240 3
52.0
8000
Total
744
So now we have two points on our demand curve.

15. 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

16. 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

17. 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

18. 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

19. The results Per-person-per-trip values are: $25 for Maumee Bay
=1/0.04
$38 for Headlands
=1/0.026

20. 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

21. 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