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:

,

0

max ( , , )

s.t.

and ( )

x v

t v

U x v q

wL x pv

T L t t v

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:

( , , ) vv f p q y

,

0

max ( , , )

s.t. and ( )x v

t v

U x v q

wL x pv T L t t v

,

0

max ( , , )

s.t. where ( )x v

v v t v

U x v q

wT x pv p p w t t

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 qualitypv

v

A

p*

v1 v2

BC

f(pv,q1+q,y)

f(pv,q1,y)

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)

( , , , , , , ) A A A AB BC Cv f p p p q q q y

Multiple sites - 2• Visiting site i gives utility• is a parameter and 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 yield in different values of ui and uj

• From 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

i i iu =f ( , p, q , y) + i

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

Zone Visits/Year Population

Visits/1000 Total travel costs

0 400 1000 400 0

1 400 2000 200 10.5

2 400 4000 100 21.0

3 400 8000 50 42.0

Visits/1000 = 300 – 7.755 * Travel Costs

An entrance fee of 10 Euro

Zone

Costs Visits/1000 Population

Visits

0 10.0 222 1000 222

1 20.5 141 2000 282

2 31.0 60 4000 240

3 52.0 0 8000 0

Total

744

So now we have two points on our demand curve.

Demand Curve

0

67

1600

744

272

0

5

10

15

20

25

30

35

40

45

Total Visitors

Addit

iona

l C

osts

/Tri

p

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

Variables

tcr -0.040 *** -0.026 ***

I ncome 0.018 0.040 ***

Sole -0.018 0.292 ***

tcs1 0.004 *** 0.005

tcs2 -0.004

Water quality -0.053 -0.139 ***

Maintenance -0.270 *** 0.033

Cleanliness 0.176 ** 0.028

Congestion -0.065 * -0.066 ***

Facilities 0.098 ** -0.004

Constant 2.648 *** 2.433 ***

R2 0.38 0.29

Sample Size 230 345

Maumee Bay Headlands

Parameter Estimates

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