The Travel Cost Model

1. The Travel Cost Model Prof. Anil Markandya Department of Economics and International Development University of Bath Environmental Economics 2 February, 24 2006

2. The Travel Cost Model (TCM) • The typical problem of the travel cost model • Basic assumptions • weak complementarity • The single site model • Poisson, Negative Binomial • The problem of on-site sampling • Example with Limdep • The multi-site model • Conditional logit model • Independence of Irrelevant alternatives

3. The demand for recreation • Objective: how revealed preference data can be used to estimate welfare changes caused by different public programs: - change in the quality of a characteristic of a recreational area (example: decrease in the level of pollution of the water at a beach) - Closure of the site (the access to the beach is forbidden) The TCM is based on REVEALED PREFERENCES

4. The origin of the TCM • Harold Hotelling (1949) “An Economic Study of the Monetary Valuation of Recreation in the National Parks,” Washington, DC: U.S. Department of the Interior, National Park Service and Recreational Planning Division. • In a letter to the US Park Service, Hotelling suggests to use TCM to assess the benefits obtained by visitors of a national park. • Intuition behind the TCM: • Need to travel to reach a site in order to enjoy it • When I decide to visit a site I need to pay a cost to reach (and enter) the site • The cost to reach (and enter) the site and the number of visits to the site allow me to estimate a lower bound of the value of the site • I estimate only use-values (non-use values can be assessed through the Contingent Valuation Method)

5. Basic assumptions • The cost of the travel and of the time spent to reach and stay at the site are a proxi for the value of the recreational experience • Use value is assessed taking into account the number of homogeneous visits to the sites among respondents Homogeneous => visits last same amount of time; I don’t want to mix 1 day visits with multi-day visits! • Visits to only one site; avoid visitors that in one day visit several sites (site A, site B, site C…) => problem to assess the welfare obtained from site A, from site B and so on

6. Weak complementarity • I assume that the environmental quality of the site affects the number of visits to the site. • I assume that if the number of visits is 0, it remains 0 even if there is a marginal increase in the quality of the site. • The weak complementarity assumption allows us to identify how the variation in a public good affects the behaviour of a person. • The idea behind the weak complementarity assumption is to link a private and a public good so that if the private good is not consumed, I cannot estimate the public good. • The basic idea behind the indirect methods of environmental valuation is to infer the monetary value of a change in the level of environmental services of interest from observed market data on some ordinary commodity.

7. The single site model • The single site model describes the demand for recreation of a person during a season (12 months) • The quantity demanded is the number of visits • The price is the cost per visit r = number of visits during a season tcr = cost of a visit Intuition: who lives close to the site has a low cost per visit. He should visit the site more often than someone who lives further away.

8. What determines the number of visits • In equation (1) we assumed that only the cost affects the number of visits. Other elements, such as age of the respondent, income, experience, availability of substitute sites may affects the number of visits: 2. tcs = price of trip to substitute site s (I expect a positive sign) y = income z = vector of socio-demographic characteristics of the respondent (age,experience, etc.) 3. B = total trip cost A+B = Willingness to pay A = consumer surplus A = Access value The ‘choke price’ is the minimum price at which the number of trips falls to zero. The consumer surplus is equal to: 4. ‘choke price’ tcr A tcr0 B r r0

9. Steps in estimating a single site model • Define the site to be valued • Define the recreation uses and seasons • Develop a sampling strategy • Specify the model • Decide on the treatment of multiple purpose trips • Design and implement the survey • Measure trip cost • Estimate the model • Calculate access value

10. Define the site to be valued • Single site model • What do we mean by “single site”? • A river • A lake • A beach • A park

11. Define the recreation uses and seasons • What are the site’s functions? Only one function? Or several functions (beach: fishing, swimming, sailing, etc.)? • Ask respondents what is their PRIMARILY purpose to visit the site • If recreation types are similar we can aggregate observations, otherwise we cannot. • when you present your results, motivate why you aggregated data from different recreation types • It can be useful to use dummy variables to take into account different recreation types • Decide the length of the season for recreation (summer, 12 months?) • Decide carefully when to do the interviews

12. Develop a sampling strategy • On-site sampling Vs off-site sampling • On-site sampling - minimize costs - fast collection of data - ‘choke price’ not identified - it is difficult that respondents remain focused on the interview => keep the questionnaire short - who shall I interview? (a person every 5…) } - the sampling plan is not representative of the population - those who visit the site more often are more likely to be surveyed Econometric problems

13. Off-site sampling (mail, telephone) - I survey both visitors and non visitors => representative of the population - ‘choke price’ is identified - expensive: difficult to intercept users - need to define the area to sample => maximum day’s drive to reach the site - if you have a registry of users, then use it => registry of anglers, hunters, etc.

14. Specify the model • Identify the variables you want to use in your model: -age, income, experience with the site and similar sites, leisure, job, education, equipment, starting point, length of the visit, number of visits, etc. - don’t ask too many questions - if on-site, no need of warm-up questions - run focus groups, talk to people at the site, to users - test the questionnaire

15. Decide on the treatment of multiple purpose trips • Goal: you want to survey daily users whose aim is to visit the site • If you are interviewing a person that does visit the site, but whose primary goal is not visiting the site (for example, visiting a friend) then you should delete this observation from the analysis

16. Design and implement the survey • The questionnaire is composed by 4 parts: - introduction - questions on visits to the site (and other substitute sites) - questions on last visit (cost, number of people travelling with, starting point, arrival, length, goal of the visit, etc.) - socio-demographic characteristics of the respondent • When to survey respondents? Not only on Saturdays and Sundays!

17. Measure trip cost - travel cost (return cost) - access fee - equipment cost - cost of time

18. Cost of time • The models to study the demand for recreation are models that study the allocation of time, therefore they are very sensitive on the assumptions on the value of time • Simple models assume it is possible to trade off leisure and work time. However, most people do not have the flexibility to shift time in and out of work in exchange for leisure.

19. Solution to the problem of time n = respondent rn = number of trips person n takes to the site tcn = travel cost and entrance fee wn = net wage per hour tn = time person n spends at the site 1) = 0 for a respondent that must work a fixed number of hours and cannot trade off leisure with work time; = 1 for a respondent that can decide how many hours to work => It is important to ask respondents what type of job they have

20. Estimate the model • Count models for the demand for recreation (Poisson, negative binomial) - Count models only consider non negative values of the dependent variable The classic count model is:

21. The Poisson model • The pdf of the Poisson is: 5. is both the mean and the variance of the distribution. It is the expected value of visits. It is assumed to be explained by the independent variables in the model (age, income, etc.) A log-linear form is useful in order to avoid negative probabilities: 6. Parameters in equation (6) are estimated by maximum likelihood: 7. Consumer surplus, or access value, for each person in the sample is: 8. is the expected number of trips for person n from equation 6

22. The negative binomial • The Poisson constrains mean and variance of r be identical: E(rn|znβ)=V(rn|znβ)=λn • Usually, in the studies of demand for recreation, the variance is larger than the mean, suggesting overdispersion of the data. As a consequence, the standard error estimated by the Poisson are underestimated => inefficient coefficients • The negative binomial is an approach for relaxing this constraint (we consider a version of the negative binomial model that is equal to a Poisson model with a gamma distributed error term in the mean): • Suppose the conditional mean from a Poisson model is the sum of znβ and an unobserved error term θn that represents unobserved individual preferences or unobserved heterogeneity: E(rn)=exp(znβ+θn) • We assume that exp(θn)=vn has a normalized gamma distribution

23. The negative binomial model: A test of α=0 is a test of H0 = Poisson model is the correct model If you find α>0 then overdispersion exists and the correct model is the negative binomial. Also if α<0 the negative binomial is the correct model. LIMDEP does the test in automatic • The mean of the negative binomial is: • The variance of the negative binomial is:

24. On-site sampling • On-site random samples are truncated at one trip and oversample more frequent users => estimates from eq. 6 are biased • Solution: Endogenous stratified and truncated Poisson • In the Poisson model the dependent variable is (r-1), rather than r. • For the negative binomial model, the correction is more complicated and you need to program into Limdep the maximum likelihood routine:

25. Calculate access value • In the Poisson model, the access value is given by assessing Sn from eq. 8. The estimate of the access value for person n is given by: • If one has estimated a Poisson model using a randomly drawn off-site sample, an estimate of aggregate access value is: where POPoff=total number of people in the relevant geographic market N=number of surveyed persons

26. If one estimates a model with an on-site sample, the aggregate access value is given by: POPon=total number of users in a season => somehow you need to find this number nj=number of persons in the sample taking j trips to the site R=largest number of trips taken by a person in the sample

27. The multi-site model • The multi-site model is not based on a “quantity demanded approach”, and describes the demand for recreation as a problem of choice among alternatives. • The model used is the random utility model (RUM). • Choices are explained by the characteristics of the sites. • We assume that respondents choose the sites that give them the highest level of utility. • This model allows to analyze the behaviour of economic agents when they are facing a problem of choosing which site to visit even when the alternative sites are many (even 1,000!)

28. Estimate of the multi-site model • Identify what we want to valuate • Define the population to sample • Define the choice set • Decide the sampling plan (on-site sampling is very troublesome) • Specify the model • Obtain information about the sites • Analysis of multi-objective visits • Data collection: I need to get information on all sites • Estimate of the cost per visit (to all sites) • Model estimates • Access value estimate

29. The random utility model • On a given choice occasion, a person considers visiting one of C sites denoted as i=1,2,3,….,C. • Each site is assumed to give the person a site utility vi. • Utilities are assumed to be a function of the trip cost and site characteristics • The utility for site i assuming a linear form is: 19. tc = trip cost of reaching site i qi is a vector of characteristics of site i ei is a random error term Site k is chosen if: 20.

30. An individual’s utility is: U = max(v0, v1, v2, v3,…,vc) V0 is the level of utility obtained by not visiting any site. To capture differences in participation, respondents’ characteristics are captured as explanatory variables in the no-trip utility function: v0 = α0+α1z+ei z is a vector of characteristics believed to influence a person’s propensity for recreation To capture differences in preferences for different sites, individual characteristics must be interacted with site characteristics.

31. Estimate the model • The probability that a person visits site k: • Pr(βtctck+ βqqk+ek≥ βtctci+ βqqi+ei for all i є C and ≥ α0+α1z+e0 ) If the error terms are IID and follow a type I extreme value distribution, equation (37) is estimated through the conditional logit model: 38. Parameters α and β are estimated by maximum likelihood: 39. where pr(i) is the logit form from eq (38) rin=1 if individual n visited site i, and =0 otherwise In circumstances where individuals are observed taking multiple trips to sites over the season, the same likelihood function is used, with rin now equal to the number of trips taken to site i by individual n

32. The restriction of Indipendence of Irrelevant Alternatives (IIA) • This restriction implies that the relative odds of choosing between any two alternatives is independent of changes that may aoccur in other alternatives in the choice set. • Model (38) violates the IIA restriction. • The Nested Logit model and the Mixed Logit model (or Random Coefficient Logit model, or Random Parameter Logit model) by introducing correlation among the site and no-trip utility error terms allow for more general patterns of substitution in the model and tehrefore relax the IIA restriction.

33. Estimate Access Value • Suppose site 1 is closed. I estimate the welfare loss for person n from the closure of site 1 per choice occasion: the negative of the coefficient on trip cost, is a measure of the marginal utility of income If person n did not visit site 1 when it was available, then the welfare loss is equal to zero • Now suppose sites 1 through 5 are closed. I estimate the welfare loss for person n from the closure of sites 1 to 5 per choice occasion:

34. Estimate the value of a quality change For a quality change the per choice occasion value for person n is: where q*i is a vector indicating a quality change at some or all of the C sites The seasonal value for each individual is the total number of choice occasions times the person’s per choice occasion value. The mean seasonal per person value is: =sample mean per choice occasion value T=total number of choice occasions in the season (number of days in the season)

35. The aggregate seasonal value over the population is: where POP is the population of users and potential users

36. Fort Phoenix - New Bedford Beach • Off site • Telephone interviews • Visits to Fort Phoenix beach, New Bedford, in 1986. • N=499 interviews

37. Number of visits (r) to Fort Phoenix beach in 1986 • Cumulative Cumulative • r Frequency Percent Frequency Percent • 0 331 66.33 331 66.33 • 1 6 1.20 337 67.54 • 2 26 5.21 363 72.75 • 3 17 3.41 380 76.15 • 4 10 2.00 390 78.16 • 5 20 4.01 410 82.16 • 6 13 2.61 423 84.77 • 7 1 0.20 424 84.97 • 8 3 0.60 427 85.57 • 10 17 3.41 444 88.98 • 12 19 3.81 463 92.79 • 13 1 0.20 464 92.99 • 14 1 0.20 465 93.19 • 15 6 1.20 471 94.39 • 16 1 0.20 472 94.59 • 18 1 0.20 473 94.79 • 20 3 0.60 476 95.39 • 24 5 1.00 481 96.39 • 25 4 0.80 485 97.19 • 30 1 0.20 486 97.39 • 35 1 0.20 487 97.60 • 36 2 0.40 489 98.00 • 40 3 0.60 492 98.60 • 48 1 0.20 493 98.80 • 50 3 0.60 496 99.40 • 90 2 0.40 498 99.80 • 92 1 0.20 499 100.00

38. Descriptive statistics x Trips to Fort Phoenix Beach in 1986 (in New Bedford, MA) BEACH 1 if respondent visited any beach in the last year, =2 otherwise pfp 1 if household has a pass tp Fort Phoenix, =0 otherwise RES 1 if the respondent resides in the Greater New Bedford area AGE Age of the respondent INC Household income in $10,000 units c1 Round-trip travel costs plus monetary value of time to nearest substitute beach cfp Round-trip travel costs plus monetary value of time to Fort Phoenix Beach c2 Round-trip travel costs plus monetary value of time to next nearest substitute beach

40. WTP for visiting Fort Phoenix • From the Poisson model, the welfare that the average person receives from visiting Fort Phoenix are given by: • WTP = 3.83/0.47 = $8.15 3.83 = average number of visits to Fort Phoenix 0.47 is the negative of the coefficient of the cost to visit Fort Phoenix • Using the negative binomial: • WTP = 3.83/0.53 = $7.22