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Valuation 9: Travel cost model PowerPoint PPT Presentation

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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

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Valuation 9: Travel cost model

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Valuation 9 travel cost model l.jpg

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

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Last week

  • Revealed preference methods

  • Defensive expenditures

  • Damage costs

  • Defensive expenditures: A simple model

  • An example: Urban ozone

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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

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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

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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:

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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:

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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











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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)

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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

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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

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  • 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

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An example

Visits/1000 = 300 – 7.755 * Travel Costs

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An entrance fee of 10 Euro

So now we have two points on our demand curve.

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  • 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

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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

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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

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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

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The results

  • Per-person-per-trip values are:

  • $25 for Maumee Bay


  • $38 for Headlands


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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

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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

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