Valuation 9: Travel cost model

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

13. An entrance fee of 10 Euro 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