Valuation 9: Travel cost model

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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

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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

pv
A
C
p
B
f(pv,q1Dq,y)
f(pv,q1,y)
v
v1
v2
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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 gt
  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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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

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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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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

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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
• 1/0.04
• 38 for Headlands
• 1/0.026

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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