Travel Cost Modeling: The Value of Enhanced Water Levels at Walker Lake to Recreational

Users

presented bypresented by

W. Douglass ShawW. Douglass Shaw

Texas A&MTexas A&M

The Problem - Background

Walker Lake is a terminus lake in Great BasinWalker Lake is a terminus lake in Great Basin fed by Walker River, a winter sport fisheryfed by Walker River, a winter sport fishery

Walker is “dying” – 140 foot decline since 1882Walker is “dying” – 140 foot decline since 1882 TDS levels have increased from 2500 mg/L in TDS levels have increased from 2500 mg/L in

1882 to 13,300 mg/L in 19941882 to 13,300 mg/L in 1994

Can something be done to restore lake levels, or Can something be done to restore lake levels, or at least halt the decline?at least halt the decline?

Walker River feeds it

But not enough…

Why Care? -- Fish Survival

Fish cannot survive above 16,000 mg/L of Fish cannot survive above 16,000 mg/L of TDSTDS

Corresponds to about a 2.3 million acre feet Corresponds to about a 2.3 million acre feet critical level (about the level at end of 1997)critical level (about the level at end of 1997) fell below this in 1992fell below this in 1992 will hit critical level within 20? yearswill hit critical level within 20? years

Recent Concerns

TDS in January, 2004 already at 15,300 ppmTDS in January, 2004 already at 15,300 ppm

Loons feed on Tui ChubLoons feed on Tui Chub

Tui Chub stopped reproducing in 2003Tui Chub stopped reproducing in 2003

Upstream Tamarisk problem (one tree, up to 200 Upstream Tamarisk problem (one tree, up to 200 gallons per day)gallons per day)

Media coverage

Project Originally Funded by U.S. Bureau of Reclamation

Data Collection: 1995-1996Data Collection: 1995-1996

Tie to Potential for Regional Water BankTie to Potential for Regional Water Bank

Elizabeth Fadali, MS from UNR (thesis), two Elizabeth Fadali, MS from UNR (thesis), two students in hydro from DRIstudents in hydro from DRI

Additional work in 1999 by Mark Eiswerth, UNRAdditional work in 1999 by Mark Eiswerth, UNR

More work in 2000 with Frank Lupi, MSUMore work in 2000 with Frank Lupi, MSU

Aside: Water Banks

Existing Water Banks in Idaho, California, Existing Water Banks in Idaho, California, New Mexico, TexasNew Mexico, Texas state runstate run deposits from farmers and ranchersdeposits from farmers and ranchers withdrawals by cities, industrywithdrawals by cities, industry

California’s most active in drought periodsCalifornia’s most active in drought periods

Supply and Demand

Supply is typically the Agricultural sector, Supply is typically the Agricultural sector, with most of the waterwith most of the water

Demand is typically the demand by hyrdo-Demand is typically the demand by hyrdo-electric power producers or recreation or electric power producers or recreation or environmental groupsenvironmental groups

Focus: Recreational Use

Uses Travel Cost/ Uses Travel Cost/ Recreation Demand ModelsRecreation Demand Models

New Feature Today: New Feature Today: Contingent Behavior Contingent Behavior ModelingModeling What What wouldwould you do if… you do if…

No Inclusion of "Non-use" No Inclusion of "Non-use" or Passive Use Valuesor Passive Use Values

Travel Cost Models

Review:Review: Q = f(P,Z), where Q is the trip, P is Q = f(P,Z), where Q is the trip, P is

the trip “price” and Z are other variables the trip “price” and Z are other variables that influence the number of trips, such as that influence the number of trips, such as the destination’s qualitythe destination’s quality

Old models: Estimate Q = a – bP + cZ Old models: Estimate Q = a – bP + cZ using ordinary least squaresusing ordinary least squares

Consumer’s Surplus and TCM

Using the predicted demand function, Using the predicted demand function, calculate the area under the demand curve calculate the area under the demand curve as “ordinary” consumer’s surplus or as “ordinary” consumer’s surplus or Marshallian welfareMarshallian welfare

More modern approach: calculate More modern approach: calculate “Hicksian” welfare measures/exact “Hicksian” welfare measures/exact consumer’s surplusconsumer’s surplus

Exact CS

Define the compensating variation (CV) for Define the compensating variation (CV) for price decrease to P’’:price decrease to P’’: V(P’,Y) = V(P’’,Y – CV), where V is V(P’,Y) = V(P’’,Y – CV), where V is

the indirect utility function, Y is incomethe indirect utility function, Y is income

Define the equivalent variation (EV) for a Define the equivalent variation (EV) for a price decrease to P’’price decrease to P’’ V(P’, Y + EV) = V(P’’,Y)V(P’, Y + EV) = V(P’’,Y)

Interpretation

CV – the amount of money that must be taken CV – the amount of money that must be taken away at the new price level, such that the person is away at the new price level, such that the person is indifferent between the original prices and the new indifferent between the original prices and the new (property right is NOT with the individual – holds (property right is NOT with the individual – holds him at the original - WTP)him at the original - WTP)

EV – amount of money individual must be EV – amount of money individual must be compensated with to forgo the change (property compensated with to forgo the change (property right IS with the individual - WTA)right IS with the individual - WTA)

Income Effects

If income effects exist, there is a price and If income effects exist, there is a price and income effect (price decrease generates income effect (price decrease generates additional “income” – but we wish to hold additional “income” – but we wish to hold that effect constant)that effect constant)

Most valuation models have no income Most valuation models have no income effects, so CV = EV = Ordinary CSeffects, so CV = EV = Ordinary CS

Uo

U1

Y

X

a

b

Price decrease in X

Surveys

Very Small Very Small Recreation Research Recreation Research BudgetBudget

Good-Sized Good-Sized "Intercept" Sample "Intercept" Sample (N = 573)(N = 573)

Yields Biased Yields Biased Sample of Sample of Recreational Users Recreational Users

On-Site Surveys

Send student crew to region lakes in 1995 Send student crew to region lakes in 1995 and 1996, in summer onlyand 1996, in summer only

Lots of effort at Lahonton, Pyramid, not Lots of effort at Lahonton, Pyramid, not just Walker Lakejust Walker Lake

Why biased sample?Why biased sample?

Biased sample

On-site (not all seasons)On-site (not all seasons) people who are more avid, more likely to people who are more avid, more likely to

be surveyed (higher probability of being be surveyed (higher probability of being intercepted)intercepted)

maybe their preferences for lakes are maybe their preferences for lakes are strongerstronger

not like the general publicnot like the general public Pyramid and Walker are winter fisheriesPyramid and Walker are winter fisheries

Innovations (statistics)

The random utility model and the count The random utility model and the count data modeldata model

Demand systems (non-normally distributed Demand systems (non-normally distributed trips)trips)

Random utility model

( , ) ( , )ji i ji j ki i ki kV Y TC Z V Y TC Z

Application of Random Utility Model Conventional Conventional

multinomial logit multinomial logit (conditional on trips (conditional on trips being fixed for the being fixed for the season):season):

1

exp( )Pr ( )

exp( )

jiji ji K

jij

Xob q Q

X

RUM Results

Fadali and Shaw, 1998 (Fadali and Shaw, 1998 (Contemporary Economic Contemporary Economic PolicyPolicy) - uses RP data only for Five Lakes) - uses RP data only for Five Lakes

Mean WTP to Prevent "Elimination" $83 per Mean WTP to Prevent "Elimination" $83 per season/personseason/person

Adjustments: Use Non-visitor WTP of only $8 per Adjustments: Use Non-visitor WTP of only $8 per seasonseason

Total Annual Value: About $4 millionTotal Annual Value: About $4 million

Conclusion: Demand/value large enough to rent Conclusion: Demand/value large enough to rent significant amounts of water from Ag Sectorsignificant amounts of water from Ag Sector

Shortcomings of Original Study

Biased Sample leads to Biased Sample leads to needed adjustmentsneeded adjustments

No exact modeling of No exact modeling of impacts of specific water impacts of specific water level changes on angling level changes on angling and other usersand other users

Model may fail to predict Model may fail to predict “out of sample” results“out of sample” results

Some New Results

See Eiswerth et al. 2000 (See Eiswerth et al. 2000 (Water Resources Water Resources ResearchResearch))

Uses Contingent Behavior Data, Walker Lake Uses Contingent Behavior Data, Walker Lake OnlyOnly

Scenarios: 20 foot increase/decline in lake level Scenarios: 20 foot increase/decline in lake level tied to Thomas (U.S.G.S., 1995)tied to Thomas (U.S.G.S., 1995)

Support of "convergent validity" -- RP and CB Support of "convergent validity" -- RP and CB data are consistent data are consistent

Contingent Behavior

Not CVM, rather:Not CVM, rather:

“ “Presume water levels rise by 20 feet at Presume water levels rise by 20 feet at Walker Lake with changed programs. Walker Lake with changed programs. Would you take more/fewer trips to Would you take more/fewer trips to Walker Lake? Elsewhere?Walker Lake? Elsewhere?

If yes, how many more/fewer?If yes, how many more/fewer?

Count Data Model

Trips (qTrips (qjiji) are not normally distributed) are not normally distributed They cannot be negativeThey cannot be negative They typically take integer valuesThey typically take integer values They can be zero (unless doing an They can be zero (unless doing an

intercept)intercept) They usually cannot exceed a value of They usually cannot exceed a value of

about 200 (day trips)about 200 (day trips)

Poisson distribution

Pr ( )!

ii

ji

e Qob q Q

Q

exp( )i X

Count Model/Contingent Behavior Results

Mean WTP for a "trip" $88Mean WTP for a "trip" $88

Values for a 1 foot increase, per person $12 - Values for a 1 foot increase, per person $12 - $18/yr$18/yr

Values for 20 foot increase $240 - $360 Values for 20 foot increase $240 - $360 /person/yr/person/yr

Totals for 20 foot increase: About $7 million to Totals for 20 foot increase: About $7 million to $13.5 per year$13.5 per year

EIS On-going/delays

Some Even Newer Results

See Fadali, Lupi and Shaw (2004)See Fadali, Lupi and Shaw (2004)

Formal Statistical Adjustment for Biased SampleFormal Statistical Adjustment for Biased Sample

Mean WTP compared to Fadali and Shaw Mean WTP compared to Fadali and Shaw drops significantlydrops significantly

WTP’s for general and on-site sample differWTP’s for general and on-site sample differ

On-site per trip WTP to prevent elimination of On-site per trip WTP to prevent elimination of Walker: $9.85 vs. “general” of $2.63Walker: $9.85 vs. “general” of $2.63