1. Valuing Changes in Environmental Amenities When the amenity is a quality characteristic of a privately consumed good The good’s price is not affected by quality

2. Exploiting “weak complementarity” A privately purchased good (some q i ) and the environmental good (b) are “weakly complementary” if individuals don’t care about b if they don’t purchase q i.

3. Weak complementarity.. often occurs in cases where b is a quality characteristic of the q Example: q = recreation trips to a lake b = water quality in that lake And individuals only care about the water quality in the lake if they use the lake for recreation (i.e. q>0)

4. Why does this help us? Area between two (compensated) demand curves for good i is: Price Quantity q i h (p,b 0,U 0 ) q i h (p,b 1,U 0 )

5. = If weak complementarity between b and q i holds then Area between demands = CV =

6. Can we actually find purchased goods that relate to environmental quality in this way? If price is bid up on units of q i with higher levels of environmental quality, then another model is appropriate (the hedonic model). This analysis requires that price not be a function of b. Possible example that fits: Water quality of regulated public water suppliers.

7. Household Production Framework – a better fit Suppose environmental quality is a quality dimension of a household produced good. The maximization decision is now: max U(q,z(x),b) + (y-pq-rx) Where z is a household produced good x is a vector of purchased inputs r is the vector of prices of x b matters only if z “produced”

8. In HPF framework If z has a constant marginal cost of production (treat as “price”) then apply previous results If not, then need to be creative… results exist that use areas between demands for an essential input into the production of z

9. Implementation Problem How do we observe behavior in the face of varying levels of environmental quality? Can not usually observe demand for a single site over time as quality varies. Often, the best we can do is look at choices across sites with varying quality.

10. Traditional Travel Cost Model of a Single Site Conceptually, can value existence of site: trips cost Individual’s lost consumer surplus from closing this site Conceptually, can value quality change at site: Individual’s demand function for trips cost trips ci0ci0 zi0zi0 ci0ci0 zi0zi0 zi1zi1 demand after quality improvement original demand function for trips Individual’s consumer surplus from improvement in site

11. Traditional Travel Cost Model Difficult to adequately account for substitutes. Difficult to capture changes in behavior in the face of changing environmental quality

12. Correlation of Substitute Prices Costs of access are often correlated across sites  imprecise estimates of cost coefficient. Consumer surplus estimate is dependent on the cost parameter. e.g. linear demand: CS = -z i 2 /2  c semilog demand: CS = -z i /  c

13. A Single Site Demand Function with Substitute Costs and Quality z ji = trips to site j by individual i c ji = costs to site j by individual i b j = quality at site j The Remaining Two Equations in this System of Demands

14. Problem with the System of Demand Equations: If the b A, b B, and b C are objective measures of site quality, then the will not vary over individuals in the sample.* *(sometimes researchers try to use perceptions for the b’s.) With no variation in these variables, coefficients can not be estimated.

15. Another problem The costs of access are often correlated across sites, making precise estimation of the “price” coefficients difficult as well.

16. The Random Utility Model has become the most popular model for modeling the choice among a finite set of alternatives with varying prices and qualities. Many, many types of applications. We will look at: recreational demand application commercial fisheries application

17. What’s the Logic Behind the RUM? On a given occasion in which the individual makes a choice among the finite set of substitutes available to him, he does so by choosing alternative j among the M alternatives, such that : U(j) = max U(m) for all m=1,…,M

18. This is a simple expression for the decision maker. But, the researcher does not observe utility nor does he observe all factors that affect utility. So he frames the problem as a stochastic one: Pr (individual i chooses alternative j) =

19. What does this systematic portion of the utility function contain? V i (m) is the “utility on the choice occasion, conditional on choosing alternative m. It is usually specified linearly as:

20. Conditional Logit vs Multinomial Logit The Random Utility Model is McFadden’s Conditional Logit. The Multinomial Logit is a related model in which the explanatory variables are individual, rather than alternative, characteristics. In the MNL, different coefficients are estimated for different alternatives, normalizing on one alternative.

21. An Example of the Difference in Models Suppose you wished to model individuals’ occupation choice: MNL: Models the choice as a function of the individual’s characteristics (e.g. age, education, parents’ education…) RUM: Models the choice as a function of the characteristics of available jobs (e.g. wage rate, education required, vacation days…)

22. The Form of the Conditional Logit (or RUM) If  im is distributed according to a Type I Extreme Value Distribution (usual assumption), Then the probability that individual i will choose alternative j is given by: (Note: this is the individual’s contribution to the likelihood function.)

23. An Important Specification Issue in the RUM Mathematically, the expression is equivalent to: If a variable does not vary over alternatives, it falls out of the specification.

24. In the current form, income falls out of the specification. (You can introduce income term non-linearly, but welfare difficult to calculate). Individual characteristics will drop out as well. (You can include them “crossed” with site specific or other site varying variables.) There is no constant term in the model. (You can include site specific constants in a similar manner to including dummy variables in regression.)

25. The Role of Income We saw that income falls out of the model in the linear form. Question: do you expect income to matter in a choice among these substitute sites? Often, it does not. Question: do you know how to measure income associated with a “choice occasion”? It’s a difficult concept. You can easily include non-linearly in model, but CV measure is very difficult to calculate.

26. Welfare Measurement Using the Simple RUM If valuing a quality change at one or more sites: Where b 0 is the original level of quality and b 1 is the subsequent level of quality.

27. For example, suppose site 1 is eliminated, then the CV measure is simply: We can also use the RUM to value the loss of a site.

28. An Increasingly Complex Example for Illustration Starting Simply…. Choice variable: Choice of beach in St Lucia, by residents of St. Lucia. Site attributes include: monetary travel cost to each site time cost to each site beach size

30. Choice Set: the alternatives that an individual views as feasible Consequences of mis-specifying the choice set: The welfare estimates will be incorrectly calculated e.g. suppose too many substitutes are included so reduced quality at a site or loss of a site is undervalued The parameter estimates may be inconsistent e.g. suppose there is an alternative of high quality, but the individual doesn’t know about it.

31. How Does One Determine What the Relevant Choice Set Should Be? Options in the literature: Distance based choice sets (Researcher defines) Parsons and Hauber Familiarity based choice sets (Respondents define) Hicks and Strand Peters, Adamowicz and Boxall Endogenous choice sets (Data define) Manski Swait and Ben-Akiva

32. What if You Have Large Number of Alternatives? Sampling Alternatives Estimates less efficient but consistent Welfare calculations require all alternatives Grouping Alternatives Deal with a smaller number of geographically aggregated sites If large variation in number of “elemental sites” across groups, then adopt Ben-Akiva and Lerman approach.

34. Coeff. Std.Err. t-ratio P-value TIMECOST -1.861.534 -3.486.00049 MONEYCOST.203.069 2.907.00365 BEACHSIZE.0004.0002 1.845.06503 Estimating a Simple Model Using the St. Lucia Data 5 alternative sites; 70 individuals Estimation performed using LIMDEP, software package of William Greene, Columbia University.

35. Interpretation of Coefficients in RUMs Not especially intuitive…..

36. Evaluating some marginal effects… Example: what’s the effect of an increase in the time costs of accessing site 1 by one hour? Choice=Site1 -26.153 - 4.67 Choice=Site2 6.168.572 Choice=Site3 5.506.572 Choice=Site4 6.068.572 Choice=Site5 8.411.572 Change in Probability Elasticity LIMDEP will calculate these for you.

37. ST1ST2ST3ST4ST5 ST152224 ST253345 ST311331 ST411222 ST5222310 Actual vs Predicted Choices ACTUALACTUAL P R E D IC T E D 23 of 70 choice predicted correctly

38. Choice-Based Sampling Random utility models depend on a random sample of the population. Parameter estimates are based on the proportion of individuals who choose different sites (conditioned on their explanatory variables). If you sample on-site, you tamper with this relationship and bias the estimated parameters.

39. Choice-Based Sampling is Sometimes the Only Feasible Survey Approach Solution to Problem: Reweighting to correct for choice-based sampling is possible if you know the following: sample proportion of interviews at site j population proportion of trips to site j

40. The Contribution to the Likelihood Function is Now… Prob of intercepting individual i at site j= where  k = ln(s k /w k )

41. The good news is…. If each site is randomly sampled and you know the proportions of total trips taken to each site (i.e. visitation rates), then LIMDEP* will do the work for you. Visitation rates can often be gotten independently either through site authorities or through a random telephone survey of the population.

42. How Much of A Difference Do Choice- Based Sampling Corrections Make? The St. Lucia study was really a choice-based sample. Visitation rates - separate random telephone survey of the population. Coeff. P-value TIMECOST-3.35.0000056 MONYCOST0.318.0000173 BEACHSZ0.0012.000000003 Coeff.P-value -1.861.00049.203.00365.00036.06503 Corrected Uncorrected

43. ST1 ST2 ST3 ST4 ST5 ST1 5 1 1 2 6 ST252239 ST310242 ST410113 ST5 2 1 1 214 No Real Improvement in Percent Predicted Correctly P R E D I C T E D ACTUALACTUAL 24 of 70 predicted correctly

44. Assessment: Choice-based sampling correction changed results Problems remain: –Wrong sign on money costs –No real improvement in proportion predicted correctly Something is still wrong

45. Suppose We Wanted to Do Welfare Measurement Using this Simple RUM? The general form of the WTP measure is: WTP i = {E[max(U i (final))]-E[max(U i (initial))]}/Mu y where: E[max(U i (initial))] = And,  1 is the marginal utility of income

46. If valuing a quality change at one or more sites: Where b 0 is the original level of quality and b 1 is the subsequent level of quality and  1 is the –1*coefficient on money cost.

47. For example, suppose site 1 is eliminated, then the WTP measure is : We can also use the RUM to value the loss of a site. Again,  1 is coefficient on money cost.

48. Welfare Measurement with RUMs Unlike the linear or semi-log regression model, the WTP measure is a function of all parameters in the model. BUT, similar to the linear and semi-log regression models, WTP is very dependent on the money cost parameter. Our estimate of the money cost parameter has the wrong sign!

49. What’s the Cause of Our Difficulties in the St Lucia Model? One Possibility: We are not taking into account differing modes of transportation by different people – car, bus, walking, so costs are not really comparable. Suppose we model the choice of mode and the choice of site simultaneously?

50. Coeff. P-value TIMECOST -.476026.00027 MONYCOST.019520.58543 BEACHSZ.000338.06473 Uncorrected for Choice-Based Sampling Results from Including 15 Alternatives: 5 sites*3 modes Coeff. P-value TIMECOST-.5492121.00298e-012 MONYCOST-.087839.00892492 BEACHSZ.0010342.88658e-015 Corrected for Choice-Based Sampling

51. A Hypothetical Policy Evaluation In an effort to raise funds to protect the beach, the authorities add a car parking fee of $5 (5.5 EURO or 2 DKK) for entrance to site 1. Using our formula for WTP the ave. loss per individual per choice occasion is only $.25 (.27 EURO or 41 DKK) in this model. There’s lots of opportunity for substitution in this model. Why so small?

52. New Hypothetical Policy Add a $5 parking fee at all sites. Average welfare loss per individual per choice occasion is now $2.25 (about 2.5 EURO or 18.50 DKK) Now, substitution is possible only through changing modes of transportation.