ological

O 1990 by S.E.L & Associates

Economic Benefits of Instream Flow to Fisheries: A Case Study of California's

Feather River

John h m i s Division of Environmental Studies

University of California-Dam3 Davis, California 95616

Joseph Cooper Department of Agricultural Economics

University of California-Davis Davis, California 95616

AEWRAm: Perfoming a benefit cost analysis of changes in instream flow requires knowledge of how the demand function shifts with changes in flow or flow related variables, such as fish catch. This paper presents a simultaneous system of demand and production equations that explicitly incorporates an instream flow variable. With this simultaneous system, the effect on recreationists' benefits of a change in iwtream flow can be directly measured. The Travel Cost Model demand equation includes the level of fish catch as the quality variable, that is, in turn, a function or river flow. The case study modeled this relationship between river flow and fishing trips to the North Fork of California's Feather River. KEY WORDS: Recreation, demand curves, travel cost method, consumer surplus, regression, fishing quality.

7? INTRODUCTlON & nsuring adequate river flows for rec- - reational fisheries on Northern Cali- fornia's Feather River is a major challenge

1 for state and federal water managers. The ' challenge lies in providing equal consid- eration for fisheries and developmental ' uses of water, For example, federal water resource agencies governed by the U.S; Water Resources Council Principles and Guidelines (WRC 1983) and the Federal Energy Regulatory Commission under the Electric Consumers Protection Act of 1986 (16 U.S.C. 791a-82% as amended), require a comparison of benefits and costs for pro- posed water projects. One way to provide equal consideration to fisheries resources is to answer thc question: How much is water worth to society when left in a par- ticular stretch of the river?

To answer this question, one first has to define the affected members of society, and, second, measure the impact. Past studies have shown that visitors to rivers such as anglers, boaters and swimmers are affected by changes in instream flow (Walsh et al. 1980; Daubert and Young.1981; Ward 1987). If Bow levels are substantially reduced, shoreline users, such as picnickers, can also be affected. When the decision is made to dam a river, even the nonvisiting general public is affected (Walsh et al. 1985).

Knowing that a broad segment of the public suffers when streamflows are re- duced begs the question of how this impact can be measured. In general, there are three theoretically correct and widcly recom- mended techniques for measuring the val- ue of environmental goods: (1) contingent

vdludtion method (CVM); (2) trdvel coat method (I'CM); and (3) hedonic property value approach (McConnc.11 1985). The CVM and TCM arc commonly used in in- stream flow studies. The first study to quantify the economic value of alternative levels of instream flow was performed by Daubert and Young (1981) using the CVM. Since then, the majority of instream flow studies have largely relied on the CVM or contingent behavior data (Loomis 1987). The CVM is a market simulation approach that asks people their net willingness to pay for alternative river flows. The method can be used to value visitors' as well as the general public's willingness topay for riv- er protection.

The TCM is a demand estimating tech- nique that quantifies visitors net willing- ness to pay for recreation. Unlike the con- tinge~~'ya1uation method, TCM relies on visitors' Bctual behavior to infer net will- ingness to pay. To perform a benefit cost analysis (BCA) of changes in recreation benefits with different instream flows, it is necessary to know how the TCM demand function shifts with changes in instream flow. However, it is often difficult to collect the needed data indicating how visitation rates actually change with flow levels. Past applications of TCM to valuing instream flow shifted the demand curves by the change in visitation rates recreationists stated they would make in response to al- ternative river levels (Narayanan et al. 1983; Ward 1987). While combining actual be- havior to estimate the underlying demand curve with intended behavior to estimate the shift in the demand curve is clever, it would be desirable to rely entirely on ac- tual behavior in estimating both the un- derlying demand curve as well as the shift in the demand curve.

The contribution of this paper is in pro- viding an approach for using actual data to estimate both the underlying demand equatioli as well as estimating how the de- mand equation is indirectly shifted with

c11d11gr.a Irt Iluw. 'l'lr~a is clo~rc by ttvtlrr$ thdt inatrerm flow ib oftvn an input to pro- , ducing fisrhing quality; that is, river flow '

intlucnccs both tlre dmourrt (e.8.. wetted j perimeter, depth of poolb) and quality of 1 habitat (e.g., water temperature). Thus, an j angler might partially judge the adequwy of river flows in terms of fishing quality. i

Of course, the river flow itself may be of additional value to the anglers in terms of

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the aesthetics of the river and vigor of ri- parian vegetation.

Nonetheless, fishing quality is certainly 1 one instream flow related variable of in- terest to the angler. While the relationship !

between instream flow and angler benefits has been measured using the CVM for steelhead trout (Johnson and Adams 1988), i it has not been measured relying only on actual behavior within the TCM frame- work. i

Incorporating fishing quality into a TCM ; to be built wing secondary data is difficult. 1 If fishing quality is measured as the total

be a function of both streamflow and the I fish catch over some period of time it may ,

number of fishing trips taken to a site. Be- cause of this simultaneity between 6sh catch and trips, proper econometric pro- cedure requires that a two equation system be estimated. One equation is the demand for trips and the other is a quasi-supply or production equation for fish catch. In the presence of simultaneity a single demand equation that includes total fish catch may result in biased and inefficient coefficient estimates. Even if the relationship between trips and catch is minimal, the estimation of these two equations simultaneously al- low the level of river Row in cubic feet per second (ds) to be explicitly incorporated as the river quality control variable. Hence,

I the effect of a change in river flow on rec- reationists' benefits can be directly mea- sured. No TCM studies allowing this direct interaction between observed visitation data and instream Row have ever been per- formed (Douglas 1987).

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THE MODEL i The economic benefit of maintaining in- in dollars above current costs a person

stream flow is measured as the visitofs would be willing to pay for the purchase i consumer surplus or net willingness to pay. of a good or service. Examples of a "good" I Consumer surplus, or maximum net will- are a fishing trip or the viewing of a wild i ingness to pay, is the maximum increase bird. Total or gross willingness to pay is :

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. . Rivers Volume 1, Number 1

tlrr aunt ol I I ~ - l amount ~ctuall the amount ac cost of ydrticip net willingneb: rxcrtss of what l'o estimate

surplus resultir flow in the sin; ing singlesite section travel needs to be estl used to estimatt ing along the ; River. Because i were not availa used. The zona. Counties of visit of visitor origil county are aggr servation. Thus vations as thert site. This compa servation TCM ber of observati individuals visi

Since many s as total fish catc seasonal or yea coefficient on si performed usin1 data; that is, ob: respond to diffel sites (Vaughan ever, the appli changes in site changes in qua

The study rivc Feather River in stre* of .the Or data were collec partmenl of Fisl provided by Pac pany. The data w on-site survey fo survey recorded angler origin, CI hours fished, ant The raw data w partment of Fish form by county ( ual anglers wert seasonal number

( J. Loomis and

ing along the North Fork of the Feather simultaneous system is specified: River. Because individual'observation data TRIPS,/POP,, = ~(TRVCOST,,, INC,,, were not available, a zonal TCM model is FISHCATCH,, used. The zonal form of the TCM utilizes counties of visitor residence as the "zones" FISHCATCH, = f(FLOW,, TRIPS,, of visitor origin. All visits from a given county are aggregated together as one ob- servation; .Thus, there are as many obser- . where: vations as there are counties visiting the i = 1,. . . , n are the number of visitor site. This compares with the. individual ob- origins. servation TCM model in which the num- . t = I , . . . , T years. ber of observations equals the number of TRVCOST,, is the transportation and individuals visiting the site. time cost of .traveling from origin i to

Since many site quality variables, such the specified site in year t. as total fish catch, are available only on a INC, .is average household income in seasonal or yearly basis, estimation of a origin i in year t. coeffiaent on site quality must usually be FISHCATCH, is a river quality vari-

CASE STUDY

The study river is the North Fork of the zonal TCM model must be used for this Feather River in Northern California, up- study. stream of the Oroville Dam. The visitation The anglers' creel, the number of fish data were collected by the California De- kept by the angler, is.incorporated into the partment of Fish and .Game with funding niodel as the fishing quality variable. The provided by Pacific Gas and Electric Com- level of creel is available for each of the pany. The data were collected using a short six separate sections of the river for each oniite survey for the years 196111985. The of the five years of the study. Therefore, survey recorded such things as county of river section specific pooled time-series

' angler origin, composition of fish catch, cross-section regressions, that include the hours fished, and fishing equipment used. creel variable for each of the river sections, The raw data were compiled by the De- can be estimated. Unlike the purely cross- partment of Fish and Game in an aggregate sectional case, where a quality coeHicient form by county of origin (i.e., the individ- can usually only be estimated with multi- URI nnglcr8 wcrc not nakc*ci to starc their ~ i t c data, the quality cocfficlcnts can bc en- : eeasonal numbcr of vi~lts). AS R result, the timatcd ~cparatcly lor each river scctlon.

. .. . . 9 . . . - .

I - a ,'An wme wctlonu arc Influenced by Irn- . . poundments, and therefore have elow

moving water, other sections are true riv- crlne environmcntu. b c h of the six river wctions is considered a eeparate recre- ational site.

Since flow data are available only for section 3, empirical results are derived only for this section. River section 3 spans the North Fork of the Feather River between Rock Creek Dam and Rock Creek power house.

The TCM model specified in this study presents trips per capita as a function of the travel expenses from a particular coun- ty of origin to the recreational site plus other monetary parameters, such as the av- erage household income for the area of or- igin, and a quality variable, such as fish catch. The model tan be specified, in time series form, as: .-

TRIPS,/POP, = Bo TRVCOST," INCdB2 - CREEL,BJ

+ u,, (3)

where:

i = 1, . . . ,57 is the number of counties in California, excluding Imperial County, from which no visitations originated over the fiveyear period of the study. t = years from 1981 to 1985. TRVCOST,, is the cost of traveling from county i to river section 3 in time t . INC, is average household income in county i in t h e t .

is the aggregate number of fish kept by anglers at river section 3 in year t .

We chose to model fishing quality as to- tal number of fish kept rather than catch per angler day primarily b e c a w we be- lieve, and other fishing research has shown (Sorg et al. 1985:5), that aggregate catch may be a better approximation of how an- glers form their perception of a river's 6sh- ing quality. That is, anglers forni their per- ceptions, concerning total b h catch, by word of mouth rather than catch per unit. The variable Labeled TRVCOST is a func-

tion of round trip distance to the site, vari- able vehicle expenses such as fuel and re- pair costs per mile, the average number of passengers per automobile, and the o p portunity cost of travel in terms of a frac-

i tion of the wrgv r,tt~'. 'I'HVCOS'I' is byrri- fied ae fdlows:

TRVCOST, - ((rtdiet fuel and 'repair CoLdb per n\ile)12.5 passengers)

; $

+ (rtdist,,/40 mph) I ('h wage rate).

Data on fuel and repair costs for each of the five years were obtained from Hertz I

Corporation surveys (Hertz News 1981- t 1986). To develop relative prices over the I

period of the study, the nominal dollar fig- t . ures were converted to real 1985 dollars. . The cost per mile in 1985 was 17 cents. ;

The secondary data require valuing trav- ; el time by the "fraction of wage rate" ap- b proach suggested by Cesario (1976) rather t

than more recent primary data approaches i suggested by Bockstael et al. (1987). The 1 value of time was calculated as one-half i the County specific wage rates in each of b the five years (California Department of Finance 1986).

The nonlinear equation (3) is mathe- maticallv eauivalent to the nonlinear in i

(1985) hrvc r~ol~rl , ur~c termine the direction of surplus cstimdir-s from 01

for uubbtitulcb. In rdd~t i t~ influencing fishing dcm. Fork of t l ~ c . 1:catltcr Hivt over the period studied. reflected by a specific ir able. We are not aware L

changes in factors affec nand other than those i~ tion (3); therefore, no ad^ have been included.

The equation for CREE

CREEL, = Bo FLOW,". (TRIPS,, / PC

where FLOW, is the ave downstream of Rock C cfs, from May to Augus t 1981-1985.

A positive correlation

the vari>blis double-log form. Model (3) is a constant elasticity model with a hom- oscedastic dependent variable. With a homoscedastic dependent variable the ad- ditive error term in equation (3) is accept- able (Judge et al. 1985).

A nonlinear form is desirable for several reasons. In general, taking the log of trips per capita has been found to reduce het- eroscedasticity (Vaughan et aL 1982; Slrong 1983). Also, the problem of a negative pre- diction of trips that can occur with a linear model is avoided with certain specifica- tions that are nonlinear in the variables or coefficients:

Since the dependent variable contains some zero observations, equation (3) must be estimated in lieu of the semi- or double log forms. To exclude counties with zero trips at some time t from the sample is equivalent to excluding relevant infor- mation from the sample and would add a truncation bias to the coefficients (Smith and Desvousges 1985).

Ideally, equation (3) should have a vari- able for price of substitute sites as there are a few substitute stream fishing areas on the west side of the Sierra Nevada Mountains; however, a substitute variable is not in- cluded in this analysis. As Caulkins et al.

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Rivers Volume 1, Number 1 January 1990

The regression results , Table 1. The results were o the TSYs Version 5.1's squares regression progra ation, this quasi-Newton : putes the approximate der spect to each of the c4

, dependent variable is the these derivatives. The dist assumed to be distributed

The Two Stage Least Sq.

Pooled time-series cross-seeti,

(1). Nonliiteitt Two Stage .Le*

INTERCEPT TRVCO!

0.001 -2.77 w.12)' (-19.58

(2) Nonlinear Least Squares r INTERCEPT FLOW

2282291 0.067 (12.35) (6.34)

' The number of observatior ' me- t-statistics are in parer.

J. Loomis and J. Cooper

(1985) have noted, one car?not a priori de- tween the level of river flow and the level temine the direction of bias in consuher of creel. In some respects, equation (4) is a surplus estimates from omitting a variable simple production function which quan- for substitutes. In addition, if other factors tifies the productivity of water in produc- influencing fishing demand on the North ing harvestable fish. While it may be de- Fork of the Feather River were changing sirable to focus on weekly or monthly flow over the period studied, they should be rather than seasonal average over the five reflected by a specific independent vari- years, we feel the fishery population dur- able. We are not aware of any significant ing a given season is more influenced by changes in factors affecting fishing de- these seasonal flows rather than weekly nand other,than those included in equa- flows as long as critical flow and temper- tion (3); thsrqfore, no additional variables ature thresholds are not exceeded. have been included. Since CREEL, is a measure of total creel ' The equation for CREEL is: in time t, it is expected that CREEL, is an

increasing function of TRIPS,, /POP,, . CREEL, = Bo FL0W,B1 Hence, there is the possibility of simul-

(TRIPS,/POP,)B2 + v,, (4) taneity between equations (3) and (4). Es- timated jointly, equations (3) and (4) form where =OW, is the avenge dixha%e a simple, yet powerful, bioemnomic SY+ downstream of Rock Creek in tem. The nonlinear format in equation (4) cfsf May to August for the yean provided a better fit of the data than a sim-

t = 1981-1985. ple linear model, which performed quite A positive correlation is expected be- poorly.

STATIS'ITCAL RESULTS

The regression m.ults are presented in timation procedure is used to estimate Table 1. The results were obtained through equations (3) and (4) as a system. The TSLS the TSIYs Version 5.1's nonlinear least regression results for equation (3) are pre- squares regression program. At each iter- sented in Table 1. Since the regression es- I ation, this quasi-Newton algorithm com- timates for equation (4) are mainly of in- putes the approximate derivatives with re- terest for estimating CREEL, for the TCM sped to each of the coefficienb. The demand equation (3), a TSLS regression is dependent variable is then regressed on not performed for equation (4). However, these derivatives. The disturbance term is for informational purposes, Table 1 also assumed to be distributed normally. presents the nonlinear least squares results

The Two Stage Least Squares (TSLS) es- for regression (4). Both regressions are

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TABLE 1 Pooled time-sen-es cross-section regressions for river section 3 of the North Fork of the Feather

River. 1 (1) Nonlinear Two Stage east Squares regression for TRIPS/POP'

I

I (2) Nonlinear Least Squares results for CREEL

'The nr~mhcr crf cth*rwntlonr In 2RS. or 5 ycnrn x 57 cnuntlm. 'The I-rtatlntlcn are In pdrrnthmrr.

TABLE 2 - 4 8 *,..I .,,..,.. n Cu,rfitrj~cr sarplu* eslrtrruli8u fur it~creusrs tn flow fur mtton 3 oJ 1l1e Nurth Fur& Frullrcr K~urr

cr oft (Itc Nortlr 1 rrr 1911. - - . Uuws a n r ~ g ~ l t -- fiah dnd mdy tr

Consumer aurplu ' CrCdu~ i t \ cdtrlf~h Morgtnal chrngr. , tity and yu~ l i t j

Total Net change per cfe T h i ~ ia not a bu:

- - I quality, how^ $108,465 ' in our analyeis. 20 cfs increase: $109,923 $1,458 $72.90 f increilsr the si. 100 cfs increase: $114,137 $5,672 $56.72

$45.70 i benefit has not t

200 cfs increase: $1 17,605 $9,140 The flow in the

BENEFITS OF ADDED INSTREAM FLOW ers, swimmers

Net economic benefits, or consumer sur- surplus when the seasonal average ob- efits need to bt plus, to the anglers are calculated using the served rate of flow in 1981 (101 cfs) is in- TSLS estimate of equation (3). The area un- creased by 20 cfs, LOO cfs and 200 cfs. These der this demand curve between the TRAV- new benefits are calculated by increasing COST at the initial level of trips and the the FLOW variable in the CREEL q u t i o n maximum observed TRAVCOST (taken as in Table 1 to predicl the new level of the vertical intempt of the demand eqw- CREEL This new level of CREEL is then tion), is the net willingness to pay, or con- inserted into the TCM demand equbtion to

m t a e l , P Amm'r~

California 1

Caulkins, I

contin

Hertz Cox

CONCLUSION AND QUALIFICATIONS

Our analysis demonstrated that a simple estimates for changes in s t r e d o w . We bic-economic system could be estimated think this is an important result because it using angler origin data. The r d b in- is based on relating actual visitation data dicated a statistically significant relation- to an actual fish catch-flow relationship. ship betwen flow and catch. Given that The economic value of instream flow re- the angler's demand function is partially ported in this paper is the value to current a function of b h catch, we derived benefit anglers from the effect of increased flow

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increase the size of fish caught, but this electricity production and the productivity benefit has not been measured in thhstudy. of the' river for some other out-of-stream

SLS for

cent

ob- s in- hese :sing ktion ?1 of then 3n to ; per TCM cse is ring efits. 1 per jle 2, arger ? that ishes . An- ,r the :h in- ional .ction ; hav-

v. We ruse it I data ;hip. 9w re- ~lrrcnt i flow

The flow in thk'river may have additional value to anglers in terms of the river's aes- thetics. Barring site congestion increases in flow and fishing quality may induce ad- ditional anglers to visit the North Fork Feather River thereby increasing recre- ational benefits. Increased streamflow is much'like a public good in that it is also. available to other river users such as boat- ers, swimmers and picnickers. These ben- efits need to be added to the $73.00 per cfs previously estimated.

To the extent that anglers represent most of the river's users and 6shing quality is

purposes. A comparison between these two values would indicate whether fish pro- duction is more inexpensively camed out using flow in the river or at a hatchery.

The estimation procedure outlined in this paper can be generalized to many possible TCM demand functions that include a vari- able(~) which measures site quality. If the site quality measure is a function of some variable that can be manipulated by a de- cision maker, then the analyst can directly estimate the changes in visitors' net eco- nomic benefits resulting from changes in' the level of this variable.

REFERENCES

Bockstael, N . I. Strand. and M. Hanemann. 1987. Time and the recreational demand model. Amen'can Iournal of Agricultural &main 69(2):293-302.

California Department of Finance. 1986. California Statistical Abstract. Sacramento: Califor- nia Department of Finance, Finance and Economic Research Unit.

Caulkins. P., Rt Bishop, and N. Bouwes. 1985. Omitted moss-price variable biases in the linear travel cost model: Correcting common misperceptions. land Economics 61(2):182- 187.

Cesario. F. 1976. The value of time in m a t i o n benefit studies..kmd Economics 52(2)32-41. Daubert, J., and R Young. 1981. Recreational demands for maintaining instieam flows: A

contingent valuation approach. American Iournal of Agricultwal Ecpnomin 63(4):666-676. Douglas, A J. 1987. Annotated bibliography of economic literature on instream flow. Fort

Collins, CO: US. Fish and Wildlife Service, National Ecology Research Center (Biological Report 881393). Available from National Technical Information Service (PB89-122436lAS).

Hertz Corporation. 1981-1986. Hntz Nnm. New York: Hertz Corporation, Public Affain Department.

Johnson, N., and R Adams. 1988. Benefits of increased streamnow: The case of the John Day River steelhead Lhery. Water Resources Rwcrrrch 24(11):1839-1846.

Judge, G., R C Hill, W. Griffiths, H. Lutkepohl, and T. C Lee. 1985. The themy and practice *

. . of econometrics. 2nd edition. New York: John Wiley and Sons.. Loomis, J. 1987. The economic value of instream flow: Methodology and benefit estimates

for optimum flows. Journal of Enoironmmtal Management 24(2):169-179. McConnell, K. 1985. The economics of outdoor recreation. Pages 677-722 in A. Kneese and

J. Sweeney, editon. Handbmk of natural rcsmrrce and energy economics. Volume 2 Nether- lands: Elsevier Science Publications.

Narayanan, R., D. Lanon, B. Bishop, and P. Amirfathi. 1983. An economic evaluation of benefits and ;rollta of maintaining instream flows. Logan: Utah State University, Utah Water Resourcen Laboratory (Water Resources Planning Srrlcs UWRLlP-(13/04).

Smith, V. K., and W. If. Ds-avoun~n. 1985. The ~~nr ra l l zed travel mt.mode1 and water qunllly bcncflk An rccrnomctdc nnnlysin. SEulhnn Krfinnmlc /nurnal52(2):371-JRI.

Soq, C., I. Loomin, D. Donnclly, C. Petemon, and L. Nelson. 1985. Net cconomlc value of

. . -. . ..,-

.f ..- !

cold and wrrm water fibhin~ In 1&1ho. Fort Collin~, CO: U.S. 1:orc.t Service, KocLy Q 1990 by S.E.L A,, Mountain Forest and h n g e Experiment Station. (Kewurce Bulletin KM-I 1).

Strong, E. 1983. A note on the functional form of travel coat modrb with unequal populations. Lui~d &currunric.s 59(3):312-349.

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U.S. Water Resources Council. 1983. Economic and rnvironmc.ntr1 principlrr for water and related land remurcer implementation studies. Washington, DC: U.S. Government Print- ing Office.

Vaughan, W., and C. Rusxll. 1982. Valuing a filrhing day: An application of a systematic varying parameter model. Land Economics 58(4):450-463.

Vaughan, W., C. Ruwell, and M. Hazilla. 1982. A note on the use of travel cost models with unequal zonal populations: Comment. Land Economics 58(3):400-407.

Walsh, R., R. Erikson, D. Arosteguy, and M. Hansen. 1980. An empi r id application of a model for estimating the recreation value of instream flow. Fort Collins: Colorado State University, Water Resources Research Institute (Report NO. 101).

Walsh, R., L. Sanders, and J. Loomis. 1985. Wild and scenic river economics: Recreation use and preservation values. Englewood, CO: American Wilderness Alliance.

I Ward, F. 1987. Economics of water allocation to instream uses in a fully appropriated river

basin: Evidence from a New Mexico wild river. Water ~evrurc& Research 23(3):381-392

Received A p d 1. 1989 Accepted May 15, 1989

Distussion open until Aug& 1, 1990

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