1. Travel Cost Modeling: The Value of Enhanced Water Levels at Walker Lake to Recreational Users presented by W. Douglass Shaw Texas A&M

2. The Problem - Background Walker Lake is a terminus lake in Great Basin Walker Lake is a terminus lake in Great Basin  fed by Walker River, a winter sport fishery Walker is “dying” – 140 foot decline since 1882 Walker is “dying” – 140 foot decline since 1882  TDS levels have increased from 2500 mg/L in 1882 to 13,300 mg/L in 1994 Can something be done to restore lake levels, or at least halt the decline? Can something be done to restore lake levels, or at least halt the decline?

3. Walker River feeds it

4. But not enough…

5. Why Care? -- Fish Survival Fish cannot survive above 16,000 mg/L of TDS Fish cannot survive above 16,000 mg/L of TDS Corresponds to about a 2.3 million acre feet critical level (about the level at end of 1997) Corresponds to about a 2.3 million acre feet critical level (about the level at end of 1997)  fell below this in 1992  will hit critical level within 20? years

6. Recent Concerns TDS in January, 2004 already at 15,300 ppm TDS in January, 2004 already at 15,300 ppm Loons feed on Tui Chub Loons feed on Tui Chub Tui Chub stopped reproducing in 2003 Tui Chub stopped reproducing in 2003 Upstream Tamarisk problem (one tree, up to 200 gallons per day) Upstream Tamarisk problem (one tree, up to 200 gallons per day)

7. Media coverage

9. Project Originally Funded by U.S. Bureau of Reclamation Data Collection: 1995-1996 Data Collection: 1995-1996 Tie to Potential for Regional Water Bank Tie to Potential for Regional Water Bank Elizabeth Fadali, MS from UNR (thesis), two students in hydro from DRI Elizabeth Fadali, MS from UNR (thesis), two students in hydro from DRI Additional work in 1999 by Mark Eiswerth, UNR Additional work in 1999 by Mark Eiswerth, UNR More work in 2000 with Frank Lupi, MSU More work in 2000 with Frank Lupi, MSU

10. Aside: Water Banks Existing Water Banks in Idaho, California, New Mexico, Texas Existing Water Banks in Idaho, California, New Mexico, Texas  state run  deposits from farmers and ranchers  withdrawals by cities, industry California’s most active in drought periods California’s most active in drought periods

11. Supply and Demand Supply is typically the Agricultural sector, with most of the water Supply is typically the Agricultural sector, with most of the water Demand is typically the demand by hyrdo- electric power producers or recreation or environmental groups Demand is typically the demand by hyrdo- electric power producers or recreation or environmental groups

12. Focus: Recreational Use Uses Travel Cost/ Recreation Demand Models New Feature Today: Contingent Behavior Modeling  What would you do if… No Inclusion of "Non-use" or Passive Use Values

13. Travel Cost Models Review: Review:  Q = f(P,Z), where Q is the trip, P is the trip “price” and Z are other variables that influence the number of trips, such as the destination’s quality Old models: Estimate Q = a – bP + cZ using ordinary least squares Old models: Estimate Q = a – bP + cZ using ordinary least squares

14. Consumer’s Surplus and TCM Using the predicted demand function, calculate the area under the demand curve as “ordinary” consumer’s surplus or Marshallian welfare Using the predicted demand function, calculate the area under the demand curve as “ordinary” consumer’s surplus or Marshallian welfare More modern approach: calculate “Hicksian” welfare measures/exact consumer’s surplus More modern approach: calculate “Hicksian” welfare measures/exact consumer’s surplus

15. Exact CS Define the compensating variation (CV) for price decrease to P’’: Define the compensating variation (CV) for price decrease to P’’:  V(P’,Y) = V(P’’,Y – CV), where V is the indirect utility function, Y is income Define the equivalent variation (EV) for a price decrease to P’’ Define the equivalent variation (EV) for a price decrease to P’’  V(P’, Y + EV) = V(P’’,Y)

16. Interpretation CV – the amount of money that must be taken away at the new price level, such that the person is indifferent between the original prices and the new (property right is NOT with the individual – holds him at the original - WTP) CV – the amount of money that must be taken away at the new price level, such that the person is indifferent between the original prices and the new (property right is NOT with the individual – holds him at the original - WTP) EV – amount of money individual must be compensated with to forgo the change (property right IS with the individual - WTA) EV – amount of money individual must be compensated with to forgo the change (property right IS with the individual - WTA)

17. Income Effects If income effects exist, there is a price and income effect (price decrease generates additional “income” – but we wish to hold that effect constant) If income effects exist, there is a price and income effect (price decrease generates additional “income” – but we wish to hold that effect constant) Most valuation models have no income effects, so CV = EV = Ordinary CS Most valuation models have no income effects, so CV = EV = Ordinary CS

18. UoUo U1U1 Y X a b Price decrease in X

19. Surveys Very Small Recreation Research Budget Very Small Recreation Research Budget Good-Sized "Intercept" Sample (N = 573) Good-Sized "Intercept" Sample (N = 573) Yields Biased Sample of Recreational Users Yields Biased Sample of Recreational Users

20. On-Site Surveys Send student crew to region lakes in 1995 and 1996, in summer only Send student crew to region lakes in 1995 and 1996, in summer only Lots of effort at Lahonton, Pyramid, not just Walker Lake Lots of effort at Lahonton, Pyramid, not just Walker Lake Why biased sample? Why biased sample?

21. Biased sample On-site (not all seasons) On-site (not all seasons)  people who are more avid, more likely to be surveyed (higher probability of being intercepted)  maybe their preferences for lakes are stronger  not like the general public  Pyramid and Walker are winter fisheries

22. Innovations (statistics) The random utility model and the count data model The random utility model and the count data model Demand systems (non-normally distributed trips) Demand systems (non-normally distributed trips)

23. Random utility model

24. Application of Random Utility Model Conventional multinomial logit (conditional on trips being fixed for the season): Conventional multinomial logit (conditional on trips being fixed for the season):

25. RUM Results Fadali and Shaw, 1998 (Contemporary Economic Policy) - uses RP data only for Five Lakes Fadali and Shaw, 1998 (Contemporary Economic Policy) - uses RP data only for Five Lakes Mean WTP to Prevent "Elimination" $83 per season/person Mean WTP to Prevent "Elimination" $83 per season/person Adjustments: Use Non-visitor WTP of only $8 per season Adjustments: Use Non-visitor WTP of only $8 per season Total Annual Value: About $4 million Total Annual Value: About $4 million Conclusion: Demand/value large enough to rent significant amounts of water from Ag Sector Conclusion: Demand/value large enough to rent significant amounts of water from Ag Sector

26. Shortcomings of Original Study Biased Sample leads to needed adjustments Biased Sample leads to needed adjustments No exact modeling of impacts of specific water level changes on angling and other users No exact modeling of impacts of specific water level changes on angling and other users Model may fail to predict “out of sample” results Model may fail to predict “out of sample” results

27. Some New Results See Eiswerth et al. 2000 (Water Resources Research) See Eiswerth et al. 2000 (Water Resources Research) Uses Contingent Behavior Data, Walker Lake Only Uses Contingent Behavior Data, Walker Lake Only Scenarios: 20 foot increase/decline in lake level tied to Thomas (U.S.G.S., 1995) Scenarios: 20 foot increase/decline in lake level tied to Thomas (U.S.G.S., 1995) Support of "convergent validity" -- RP and CB data are consistent Support of "convergent validity" -- RP and CB data are consistent

28. Contingent Behavior Not CVM, rather: Not CVM, rather:  “Presume water levels rise by 20 feet at Walker Lake with changed programs. Would you take more/fewer trips to Walker Lake? Elsewhere?  If yes, how many more/fewer?

30. Count Data Model Trips (q ji ) are not normally distributed Trips (q ji ) are not normally distributed  They cannot be negative  They typically take integer values  They can be zero (unless doing an intercept)  They usually cannot exceed a value of about 200 (day trips)

31. Poisson distribution

32. Count Model/Contingent Behavior Results Mean WTP for a "trip" $88 Mean WTP for a "trip" $88 Values for a 1 foot increase, per person $12 - $18/yr Values for a 1 foot increase, per person $12 - $18/yr Values for 20 foot increase $240 - $360 /person/yr Values for 20 foot increase $240 - $360 /person/yr Totals for 20 foot increase: About $7 million to $13.5 per year Totals for 20 foot increase: About $7 million to $13.5 per year

33. EIS On-going/delays

35. Some Even Newer Results See Fadali, Lupi and Shaw (2004) See Fadali, Lupi and Shaw (2004) Formal Statistical Adjustment for Biased Sample Formal Statistical Adjustment for Biased Sample  Mean WTP compared to Fadali and Shaw drops significantly WTP’s for general and on-site sample differ WTP’s for general and on-site sample differ  On-site per trip WTP to prevent elimination of Walker: $9.85 vs. “general” of $2.63