1. 1 Subjective Probability Travel Costs Scott Matthews Courses: 12-706 / 19-702

2. 12-706 and 73-3592 Admin Issues  HW 4 back today  HW 5 due next Wed  Next project due Nov 16  Case studies coming

3. 12-706 and 73-3593 Subjective Probabilities  Main Idea: We all have to make personal judgments (and decisions) in the face of uncertainty (Granger Morgan’s career)  These personal judgments are subjective  Subjective judgments of uncertainty can be made in terms of probability  Examples:  “My house will not be destroyed by a hurricane.”  “The Pirates will have a winning record (ever).”  “Driving after I have 2 drinks is safe”.

4. 12-706 and 73-3594 Outcomes and Events  Event: something about which we are uncertain  Outcome: result of uncertain event  Subjectively: once event (e.g., coin flip) has occurred, what is our judgment on outcome?  Represents degree of belief of outcome  Long-run frequencies, etc. irrelevant - need one  Example: Steelers* play AFC championship game at home. I Tivo it instead of watching live. I assume before watching that they will lose.  *Insert Cubs, etc. as needed (Sox removed 2005)

5. 12-706 and 73-3595 Next Steps  Goal is capturing the uncertainty/ biases/ etc. in these judgments  Might need to quantify verbal expressions (e.g., remote, likely, non-negligible..)  What to do if question not answerable directly?  Example: if I say there is a “negligible” chance of anyone failing this class, what probability do you assume?  What if I say “non-negligible chance that someone will fail”?

6. 12-706 and 73-3596 Merging of Theories  Science has known that “objective” and “subjective” factors existed for a long time  Only more recently did we realize we could represent subjective as probabilities  But inherently all of these subjective decisions can be ordered by decision tree  Where we have a gamble or bet between what we know and what we think we know  Clemen uses the basketball game gamble example  We would keep adjusting payoffs until optimal

7. 12-706 and 73-3597 Probability Wheel  Mechanism for formalizing our thoughts on probabilities of comparative lotteries  You select the area of the pie chart until you’re indifferent between the two lotteries  Quick 2-person exercise. Then we’ll discuss p-values.

8. 12-706 and 73-3598 Continuous Distributions  Similar to above, but we need to do it a few times.  E.g., try to get 5%, 50%, 95% points on distribution  Each point done with a “cdf-like” lottery comparison

9. 12-706 and 73-3599 Danger: Heuristics and Biases  Heuristics are “rules of thumb”  Which do we use in life? Biased? How?  Representativeness (fit in a category)  Availability (seen it before, fits memory)  Anchoring/Adjusting (common base point)  Motivational Bias (perverse incentives)  Idea is to consider these in advance and make people aware of them

10. 12-706 and 73-35910 Asking Experts  In the end, often we do studies like this, but use experts for elicitation  Idea is we should “trust” their predictions more, and can better deal with biases  Lots of training and reinforcement steps  But in the end, get nice prob functions

11. 12-706 and 73-35911

12. Travel Costs Scott Matthews 12-706 / 19-702 / 73-359

13. 12-706 and 73-35913 Travel Costs  Time is a valuable commodity (time is $)  Arguably the most valuable  All about opportunity cost  Most major transportation/infrastructure projects built to ‘save travel costs’  Need to tradeoff project costs with benefits  Ex: new highway that shortens commutes  Differences between ‘travel’ and ‘waiting’  Waiting time disutility might be orders of magnitude higher than just ‘travel disutility’  Why? Travelling itself might be fun

14. 12-706 and 73-35914 Valuation: Travel Cost Method  Estimate economic use values associated with ecosystems or sites that are used for recreation  changes in access costs for a recreational site  elimination of an existing recreational site  addition of a new recreational site  changes in environmental quality  www.ecosystemvaluation.org/travel_costs.htm

15. 12-706 and 73-35915 Travel Cost Method  Basic premise - time and travel cost expenses incurred to visit a site represent the “price” of access to the site.  Thus, peoples’ WTP to visit the site can be estimated based on the number of trips that they make at different travel costs.  This is analogous to estimating peoples’ WTP for a marketed good based on the quantity demanded at different prices.

16. 12-706 and 73-35916 Example Case  A site used mainly for recreational fishing is threatened by development.  Pollution and other impacts from this development could destroy the fish habitat  Resulting in a serious decline in, or total loss of, the site’s ability to provide recreational fishing services.  Resource agency staff want to determine the value of programs or actions to protect fish habitat at the site.

17. 12-706 and 73-35917 Why Use Travel Cost?  Site is primarily valuable to people as a recreational site. There are no endangered species or other highly unique qualities that would make non-use values for the site significant.  The expenditures for projects to protect the site are relatively low. Thus, using a relatively inexpensive method like travel cost makes the most sense.  Relatively simple compared to other methods

18. 12-706 and 73-35918 Options for Method  A simple zonal travel cost approach, using mostly secondary data, with some simple data collected from visitors.  An individual travel cost approach, using a more detailed survey of visitors.  A random utility approach using survey and other data, and more complicated statistical techniques.

19. 12-706 and 73-35919 Zonal Method  Simplest approach, estimates a value for recreational services of the site as a whole. Cannot easily be used to value a change in quality of recreation for a site  Collect info. on number of visits to site from different distances. Calculate number of visits “purchased” at different “prices.”  Used to construct demand function for site, estimate consumer surplus for recreational services of the site.

20. 12-706 and 73-35920 Zonal Method Steps  1. define set of zones around site. May be defined by concentric circles around the site, or by geographic divisions, such as metropolitan areas or counties surrounding the site  2. collect info. on number of visitors from each zone, and the number of visits made in the last year.  3. calculate the visitation rates per 1000 population in each zone. This is simply the total visits per year from the zone, divided by the zone’s population in thousands.

21. 12-706 and 73-35921 Sample Data

22. 12-706 and 73-35922 Estimating Costs z 4. calculate average round-trip travel distance and travel time to site for each zone. y Assume Zone 0 has zero travel distance and time. y Use average cost per mile and per hour of travel time, to calculate travel cost per trip. y Standard cost per mile is $0.30. The cost of time is from average hourly wage. y Assume that it is $9/hour, or $.15/minute, for all zones, although in practice it is likely to differ by zone.

23. 12-706 and 73-35923 Data 5. Use regression to find relationship between visits and travel costs, e.g. Visits/1000 = 330 – 7.755*(Travel Cost) “a proxy for demand given the information we have”

24. 12-706 and 73-35924 Final steps  6. construct estimated demand for visits with regression. First point on demand curve is total visitors to site at current costs (with no entry fee), which is 1600 visits. Other points by estimating number of visitors with different hypothetical entrance fees (assuming that an entrance fee is valued same as travel costs). Start with $10 entrance fee. Plugging this into the estimated regression equation, V = 330 – 7.755C:

25. 12-706 and 73-35925 Demand curve zThis gives the second point on the demand curve—954 visits at an entry fee of $10. In the same way, the number of visits for increasing entry fees can be calculated:

26. 12-706 and 73-35926 Graph Consumer surplus = area under demand curve = benefits from recreational uses of site around $23,000 per year, or around $14.38 per visit ($23,000/1,600). Agency’s objective was to decide feasibility to spend money to protect this site. If actions cost less than $23,000 per year, the cost will be less than the benefits provided by the site.

27. 12-706 and 73-35927 Recreation Benefits  Value of recreation studies  ‘Values per trip’ -> ‘value per activity day’  Activity day results (Sorg and Loomis 84)  Sport fishing: $25-$100, hunting $20-$130  Camping $5-$25, Skiing $25, Boating $6-$40  Wilderness recreation $13-$75  Are there issues behind these results?

28. 12-706 and 73-35928 Value of travel time savings  Many studies seek to estimate VTTS  Can then be used easily in CBAs  Waters, 1993 (56 studies)  Many different methods used in studies  Route, speed, mode, location choices  Results as % of hourly wages not a $ amount  Mean value of 48% of wage rate (median 40)  North America: 59%/42%  Good resource for studies like this: www.vtpi.org

29. 12-706 and 73-35929 Government Analyses  DOT (1997): Use % of wage rates for local/intercity and personal/business travel  These are the values we will use in class Office of Secretary of Transportation, “Guidance for the Valuation of Travel Time in Economic Analysis”, US DOT, April 1997.

30. 12-706 and 73-35930 In-and-out of vehicle time

31. 12-706 and 73-35931 Income and VTTS  Income levels are important themselves  VTTS not purely proportional to income  Waters suggests ‘square root’ relation  E.g. if income increases factor 4, VTTS by 2

32. 12-706 and 73-35932 Introduction - Congestion  Congestion (i.e. highway traffic) has impacts on movement of people & goods  Leads to increased travel time and fuel costs  Long commutes -> stress -> quality of life  Impacts freight costs (higher labor costs) and thus increases costs of goods & services  http://mobility.tamu.edu/

33. 12-706 and 73-35933 Literature Review  Texas Transportation Institute’s 2005 Annual Mobility Report  http://tti.tamu.edu/documents/mobility_report_2005.pdf  20-year study to assess costs of congestion  Average daily traffic volumes  Binary congestion values  ‘Congested’ roads assumed both ways  Assumed 5% trucks all times/all roads  Assumed 1.25 persons/vehicle, $12/hour  Assumed roadway sizes for 3 classes of roads  Four different peak hour speeds (both ways)

34. 12-706 and 73-35934 Results  An admirable study at the national level  In 2003, congestion cost U.S. 3.7 billion hours of delay, 2.3 billion gallons of wasted fuel, thus $63 billion of total cost

35. 12-706 and 73-35935 Long-term effects (Tufte?) Uncongested 33% Severe 20% Heavy 14%

36. 12-706 and 73-35936 Old / Previous Results  Method changed over time..  In 1997, congestion cost U.S. 4.3 billion hours of delay, 6.6 billion gallons of wasted fuel, thus $72 billion of total cost  New Jersey wanted to validate results with its own data

37. 12-706 and 73-35937 New Jersey Method  Used New Jersey Congestion Management System (NJCMS) - 21 counties total  Hourly data! Much more info. than TTI report  For 4,000 two-direction links  Freeways principal arteries, other arteries  Detailed data on truck volumes  Average vehicle occupancy data per county, per roadway type  Detailed data on individual road sizes, etc.

38. 12-706 and 73-35938 Level of Service  Description of traffic flow (A-F)  A is best, F is worst (A-C ‘ok’, D-F not)  Peak hour travel speeds calculated  Compared to ‘free flow’ speeds  A-C classes not considered as congested  D-F congestion estimated by free-peak speed  All attempts to make specific findings on New Jersey compared to national  http://www.njit.edu/Home/congestion/

39. 12-706 and 73-35939 Definitions  Roadway Congestion Index - cars per road space, measures vehicle density  Found per urban area (compared to avgs)  > 1.0 undesirable  Travel Rate Index  Amount of extra time needed on a road peak vs. off-peak (e.g. 1.20 = 20% more)

40. 12-706 and 73-35940 Definitions (cont.)  Travel Delay - time difference between actual time and ‘zero volume’ travel time  Congestion Cost - delay and fuel costs  Fuel assumed at $1.28 per gallon  VTTS - used wage by county (100%)  Also, truck delays $2.65/mile (same as TTI)  Congestion cost per licensed driver  Took results divided by licenses  Assumed 69.2% of all residents each county

41. 12-706 and 73-35941 Details  County wages $10.83-$23.20 per hour  Found RCI for each roadway link in NJ  Aggregated by class for each county

42. 12-706 and 73-35942 RCI result: Northern counties generally higher than southern counties New York City

43. 12-706 and 73-35943 TRI result: Northern counties generally higher than southern counties

44. 12-706 and 73-35944

45. 12-706 and 73-35945 Avg annual Delay = 34 hours! Almost a work Week!

46. 12-706 and 73-35946

47. 12-706 and 73-35947 Effects  Could find annual hours of delay per driver by aggregating roadway delays  Then dividing by number of drivers  Total annual congestion cost $4.9 B  Over 5% of total of TTI study  75% for autos (190 M hours, $0.5 B fuel cost)  25% for trucks (inc. labor/operating cost)  Avg annual delay per driver = 34 hours

48. 12-706 and 73-35948

49. 12-706 and 73-35949 Future  Predicted to only get worse  Congestion costs will double by 2015