Subjective Probability Travel Costs

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Subjective ProbabilityTravel Costs

• Scott Matthews
• Courses 12-706 / 19-702

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Admin Issues

• HW 4 back today
• HW 5 due next Wed
• Next project due Nov 16
• Case studies coming

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Subjective Probabilities

• Main Idea We all have to make personal
  judgments (and decisions) in the face of
  uncertainty (Granger Morgans 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.

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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)

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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?

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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

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Probability Wheel

• Mechanism for formalizing our thoughts on
  probabilities of comparative lotteries
• You select the area of the pie chart until youre
  indifferent between the two lotteries
• Quick 2-person exercise. Then well discuss
  p-values.

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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

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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

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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

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Travel Costs

• Scott Matthews
• 12-706 / 19-702 / 73-359

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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

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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

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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.

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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 sites 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.

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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

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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.

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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.

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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 zones population in thousands. 

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Sample Data
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Estimating Costs

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

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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
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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

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Demand curve

• This gives the second point on the demand
  curve954 visits at an entry fee of 10.  In the
  same way, the number of visits for increasing
  entry fees can be calculated

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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).  Agencys 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.
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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?

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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

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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.
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In-and-out of vehicle time
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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

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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/

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Literature Review

• Texas Transportation Institutes 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)

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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

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Long-term effects (Tufte?)
Uncongested 33
Severe 20
Heavy 14
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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

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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.

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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/

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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)

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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

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Details

• County wages 10.83-23.20 per hour
• Found RCI for each roadway link in NJ
• Aggregated by class for each county

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New York City
RCI result Northern counties generally
higher than southern counties
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TRI result Northern counties generally
higher than southern counties
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Avg annual Delay 34 hours! Almost a work Week!
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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

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Future

• Predicted to only get worse
• Congestion costs will double by 2015