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Applications of SimulationTravel Costs

Scott MatthewsCourses: 12-706 / 19-702

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Admin Issues

No Friday class this weekMore on HW 4 – removing Q #17.

Will show updated grade range Wed (regrades)Today: @RISK tutorial, stochastic dominanceNeed to specify take-home final plans

Week of Dec 8-12, Two timeslots? #1: Morning of 8th – 5pm on 10th

#2: Morning of 10th – 5pm on 12th

@RISK tutorial/simulations

@RISK the “most different” of the plugins in latest version Please look at the online materials (not

just book tutorial) since various things different.

Another current application: www.fivethirtyeight.com

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Stochastic Dominance “Defined”

A is better than B if:Pr(Profit > $z |A) ≥ Pr(Profit > $z |B),

for all possible values of $z.Or (complementarity..)Pr(Profit ≤ $z |A) ≤ Pr(Profit ≤ $z |B),

for all possible values of $z.A FOSD B iff FA(z) ≤ FB(z) for all z

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Stochastic Dominance:Example #1CRP below for 2 strategies shows

“Accept $2 Billion” is dominated by the other.

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Stochastic Dominance (again) Chapter 4 (Risk Profiles) introduced deterministic and

stochastic dominance We looked at discrete, but similar for continuous How do we compare payoff distributions? Two concepts: A is better than B because A provides unambiguously higher

returns than B A is better than B because A is unambiguously less risky than B If an option Stochastically dominates another, it must have a

higher expected value

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First-Order Stochastic Dominance (FOSD) Case 1: A is better than B because A provides

unambiguously higher returns than B Every expected utility maximizer prefers A to B (prefers more to less) For every x, the probability of getting at least x is higher

under A than under B. Say A “first order stochastic dominates B” if:

Notation: FA(x) is cdf of A, FB(x) is cdf of B. FB(x) ≥ FA(x) for all x, with one strict inequality or .. for any non-decr. U(x), ∫U(x)dFA(x) ≥ ∫U(x)dFB(x) Expected value of A is higher than B

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FOSD

Source: http://www.nes.ru/~agoriaev/IT05notes.pdf

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FOSD Example

Option A Option B

Profit ($M) Prob.

0 ≤ x < 5 0.25 ≤ x < 10 0.310 ≤ x < 15

0.4

15 ≤ x < 20

0.1

Profit ($M) Prob.

0 ≤ x < 5 05 ≤ x < 10 0.110 ≤ x < 15

0.5

15 ≤ x < 20

0.3

20 ≤ x < 25

0.1

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First-Order Stochastic Dominance

00.20.40.60.8

1

0 5 10 15 20 25Profit ($millions)

Cumulative Probability

AB

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Second-Order Stochastic Dominance (SOSD) How to compare 2 lotteries based on risk

Given lotteries/distributions w/ same mean So we’re looking for a rule by which we can say “B

is riskier than A because every risk averse person prefers A to B”

A ‘SOSD’ B if For every non-decreasing (concave) U(x)..

€

U(x)dFA (x)0

x

∫ ≥ U(x)dFB (x)0

x

∫

€

[FB (x) − FA (x)]dx0

x

∫ ≥ 0,∀x

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SOSD Example

Option A Option B

Profit ($M) Prob.

0 ≤ x < 5 0.15 ≤ x < 10 0.310 ≤ x < 15

0.4

15 ≤ x < 20

0.2

Profit ($M) Prob.

0 ≤ x < 5 0.35 ≤ x < 10 0.310 ≤ x < 15

0.2

15 ≤ x < 20

0.1

20 ≤ x < 25

0.1

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Second-Order Stochastic Dominance

00.20.40.60.8

1

0 5 10 15 20 25Profit ($millions)

Cumulative Probability

AB

Area 2

Area 1

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SOSD

Travel Costs

Scott Matthews12-706 / 19-702

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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 MethodEstimate 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 MethodBasic 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

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.

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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 MethodSimplest 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 zone’s population in thousands. 

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Sample Data 

Zone TotalVisits/Year

ZonePopulation

Visits/1000

0 400 1000 4001 400 2000 2002 400 4000 1003 400 8000 50

Beyond 3 0Total Visits 1600

   

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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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DataZone Round

Trip Dist .Rou ndTrip Time

Dist ancetime s

Cost /Mile($.30)

Trave lTimetime s

Cost /Minute($.15)

TotalTrave lCost /Trip

0 0 0 0 0 01 20 30 $6 $4.50 $10.502 40 60 $12 $9.00 $21.003 80 120 $24 $18.00 $42.00

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:

Zone Travel Costplus $10

Visits/1000 Population Total Visits

0 $10 252 1000 2521 $20.50 171 2000 3422 $31.00 90 4000 3603 $52.00 0 8000 0

Total Visits 954

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Demand curve

This 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:

Entry Fee Total Visits$20 409$30 129$40 20$50 0

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GraphConsumer 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.

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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 savingsMany studies seek to estimate VTTS

Can then be used easily in CBAsWaters, 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 ofTravel 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 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)

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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?)

Uncongested33%

Severe20%

Heavy14%

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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 MethodUsed New Jersey Congestion Management

System (NJCMS) - 21 counties totalHourly data! Much more info. than TTI report

For 4,000 two-direction linksFreeways 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 ServiceDescription 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 timeCongestion 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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RCI result:

Northern counties generally higherthan southerncounties

New YorkCity

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TRI result:

Northern counties generally higherthan southerncounties

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Avg annualDelay = 34 hours!

Almost a workWeek!

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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 Why? We spend money on construction