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 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:

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:

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

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)

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

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 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 – 7.755 * Travel Costs

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.

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

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