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AN ABSTRACT OF THE THESIS OF Ching-Kai Hsiao in for the degree of Agricultural Resource and Doctor of Philosophy Presented Economics on April 30, 1985. Title: An Evaluation of Alternative Estimates of Demand for and Benefits from Oregon Salmon Sport Fishing. Redacted for privacy Abstract approved: William G. Brown The main objective of this study was to estimate the demand sport for fishing. travel cost method was used The primary technique for demand analysis. estimates salmon and net econcinic benefits from Oregon Several as the empirical of consumer surplus per trip and per fish were obtained from different estimation methods. The differences different versions observation travel bias this cost travel the approaches produced higher than costs economic of among benefits economic were method Empirical results indicated that the individual assessed. estimates net in the zone average approach of net are believed to be due in part to the caused by travel cost of surplus reported when These higher estimates were used. benefits problem consumer bias measurement was instrumental variable approach. dealt with error. by However, using the Higher resulted estimates from observations function net use of economic unadjusted individual demand recreational for fitting the (Ulo) also benefits because this approach does not account declining the for participation rates for the more distant zones. Therefore, it observations the the of recommended is individual the that be adjusted to a per capita basis, probability participation be linked to of that or UlO the estimates of demand in order to compute valid estimates of net economic .benef its. A and quality hedonic variable was incorporated into regional and marginal Average travel cost models. values of the primary site and substitutes sites thus were directly derived from the demand equations. Estimates computed from changed and total and average consumer of the very little with the addition of quality regional variables in the more travel cost models. model cost traditional travel surpluses substitute the completely specified This finding indicates that the traditional travel cost model may be basically for estimating However, total additional and were average research on consumer robust surplus. recreational other activities is needed to see if estimates of total consumer surplus remain from the relatively variables traditional travel cost stable when quality model and always substitute are included in a regional travel cost type specification. of Unfortunately, the numerical estimates of value per were trip and per fish from the hedonic travel cost model rather unstable and should questionable for this study. marginal values be considered Similarly, somewhat the estimates of per fish from the regional travel cost model did not seem very reasonable, being only about one- fourth fish. appears of the average value per Therefore, it that the more complex regional and hedonic travel cost models require more and better quality data to more accurate estimates of marginal values per fish. yield An Evaluation of Alternative Estimates of Demand for and Benefits from Oregon Salmon Sport Fishing by Ching-Kai Hsiao A THESIS submitted to Oregon State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy Completed Commencement April 30, 1985 June 9, 1985 APPROVED: Redacted for privacy Professor of Agricultural and Resource Economics in charge of major Redacted for privacy Head of Department of Agricultural and Resource Economics Redacted for privacy Date thesis is. presented April 30, 1985 Typed by Shih-Ya Yeh and Ching.-Kai Hsiao for Ching-Kai Hsiao ACKNOWLEDGEMENTS This study was made possible by the and assistance of many people. encouragement Gratitude and appreciation are due to the members of the graduate advisory committee, Dr. Richard Adams, Dr. William Brown, Dr. Dale Mcfarlane, Dr. Wesley Musser, and Dr. David Thomas, who assisted the completion of this thesis. A special thanks is extended to Dr. William Brown for his guidance and assistance as major professor. I would like to dedicate this thesis to my parents for their understanding and support, to my son 1-Ming for his encouraging smile, Shih-Ya, whose and especially to my lovely emotional support and were essential to completing this study. constructive wife help TABLE OF CONTENTS Chapter Page INTRODUCTION Statement of the Problem Objectives Methodology Source of Data Outline for Presentation of Research in this Study THE THEORETICAL IN CONSIDERATIONS SPECIFICATION OF DEMAND FOR OUTDOOR RECREATION A Model of Demand Analysis for Outdoor Recreation The Specification Problem The Identification Problem Evaluation Methods of Demand for Outdoor Recreation Comparison of Various Evaluation Methods Measures of Consumer Welfare The Travel Cost Method 1 2 7 8 9 10 SOME EMPIRICAL ESTIMATES OF SINGLE SITE TYPES OF TRAVEL COST DEMAND FOR OREGON SALMON ANGLING Estimated Zone Average Travel Cost Demand Fresh-Water Salmon Sport Fishing Ocean Salmon Sport Fishing Theoretical Relationships Between Angler Benefits and Fish Catch Relation of Estimated Angler Benefits to Salmon Catch Effect of Other Factors Upon Estimated Benefits Per Fish Estimated Adjusted Individual Travel Cost Demand Fresh-Water Salmon Sport Fishing Ocean Salmon Sport Fishing Estimated Unadjusted Individual Travel Cost Demand Fresh-Water Salmon Sport Fishing Ocean Salmon Sport Fishing DISCUSSION AND APPRAISAL OF SEVERAL VERSIONS OF THE TRAVEL COST METHOD Individual Observations Versus Zonal Averages Reasons for Declining Participation Rates 13 14 17 20 22 22 26 30 34 34 35 40 41 44 49 54 55 59 60 61 63 65 66 68 TABLE OF CONTENTS (cont.) Chapter Page Effects of Distance Upon Participation Rate in Ocean Salmon Fishing Measurement Errors in Travel Cost Variable Sources and Consequences of Measurement Errors The Instrumental Variable Approach 74 81 82 85 INCLUSION OF QUALITY VARIABLES IN THE TRAVEL COST MODEL Using Regional Travel Cost Models to Estimate the Benefits from Fresh-Water Salmon Fishing Regional Travel Cost Method Estimation of Regional Travel Cost Demand Model Use of the Hedonic Travel Cost Model to Estimate the Value of Site Characteristics Hedonic Travel Cost Method Estimation of Hedonic Travel Cost Demand Model SUMMARY AND CONCLUSIONS 91 91 92 96 103 104 109 116 BIBLIOGRAPHY 129 APPENDIX A 139 APPENDIX B 140 APPENDIX C 144 APPENDIX D 145 APPENDIX E 150 APPENDIX F 156 LIST OF TABLES Page Table 1 2 3 4 5 6 Estimated net economic benefits and catch for Oregon fresh-water salmon sport anglers average zonal in 1977, upon based participation rates per capita 39 Estimated net economic benefits and catch f or Oregon fresh-water salmon sport anglers individual in 1977, based upon participation rates per capita 57 Observations zones generated for three distance 70 Estimated consumer surplus to ocean salmon sport anglers of Oregon, based upon four different methods of estimation 80 Estimated consumer surplus to ocean salmon anglers of Oregon, based upon observed travel cost variable and its instrumental variable 89 Estimated net economic benefits for Oregon fresh-water salmon sport anglers in 1977, based upon regional travel cost method 98 7 A comparison of consumer surplus values for fresh-water salmon sport fishing, estimated by various models using reported travel 117 costs 8 A comparison of consumer surplus values for ocean salmon sport fishing, estimated by various models using reported travel costs 117 9 A comparison of consumer surplus values for ocean salmon sport fishing, estimated by 119 various models using measured distance F-i Some regression results and .the estimates Gum-Martin consumer surplus for Oregon 157 fresh-water salmon angling in 1977 of AN AND EVALUATION OF ALTERNATIVE ESTIMATES OF DEMAND FOR BENEFITS FROM OREGON SALMON SPORT FISHING I. Leisure is one INTRODUCTION of the fast growing industries. Almost all Western and Eastern countries maintain research centers on leisure (Kaplan, 1975). the In 1958, U.S. Congress enacted and President Eisenhower signed into Resources document to establish the Outdoor Recreation Review seven the Commission (ORRRC). Early in the law 1960s, twenty- reports were produced by a staff of 100 persons ORRRC. Shortly thereafter, Recreation was established Not been only recognized, the Bureau of of Outdoor under President Kennedy. has the importance of outdoor recreation but participation in outdoor recreation has been increasing rapidly. been The major factors have increased total population, higher real income per capita, greater leisure time, and more travel (Clawson, 1959). Indeed, "the outdoors has always been and is still a great laboratory for learning, playground people other for wholesome fun and hike, enjoyment. It affords a special kind of fulfillment not available in any setting. Thus, deer in the forests, groves and a a museum for study, in there must be fish in the scenery to paint and to which to camp and picnic, wilderness to explore, rivers, photograph, trails on which and pleasant places in to our 2 cities, more Yes, them. we if are to retain them we must work we must than that, plan, for coordinate, cooperate, and educate." (Jensen, 1973, pp.v-vi) Statement of the Problem The economists' interest in an economic problem has to place valuations on it. arisen because resources volume of is the valuation has This need for for land water and and but the area of land water are essentially fixed. as need largely developed from the competition increasing, outdoor recreation For the sake the of optimum allocation of scarce resources, all the valuations analyzed and choices among various alternatives should be to compete for the scarce means. Just as Clawson said "... it is customary to measure the economic or monetary gains and costs of each use of land or water. If this process is and if recreation is to considered in the same manner as alternative uses of the resources, then a value must be put on the amount of to be carried to its conclusion, be recreation provided." (Clawson, 1959, p.2). On the other hand, as resource planners become more aware of the importance of outdoor recreational activities and as resources capable of providing outdoor opportunities diminish, the concept of recreation demand becomes increasingly important. Not only the planners and decison- 3 makers are meeting the challenge by greater demand analyses turning (such and their and descriptive from as the social characteristics of anglers, park-goers) to search for the underlying on now are but researchers studies, attention away emphasis studies hunters, behavioral components of such participation. Moreover, while the prices of goods or services can usually be determined through the market mechanism system, the value of nonmarket goods or services recreation cannot Therefore, valuation difficult. Although methods that be calculated of like outdoor via the market system. nonmarket goods or services there are a number have been proposed for of is measurement evaluating outdoor recreation, only a few of them have been proved correct in specification and estimation. "Oregon's habitat for diverse geography provides the a wide variety of fish and necessary wildlife. renewable resource is one of the most valuable assets state has millions and of individuals each year " 1979-1980, p.188) are it provides recreation and jobs fish are Blue ( Oregon the many Book, As for these resources, anadromous fish the most valuable segment of these to This dependent Oregon's absolutely fishery, upon and continuing satisfactory habitat in which to carry out the fresh-water phase chinook of their life cycle. As a matter salmon-- a distinctive economic and of fact, the recreational asset-- was declared the state fish by the Oregon 1961 legislature For the commercial fishery, records are on kept landings and the yield is marketed on a per unit basis, monetary But value for these fish can be reliably for sport fishing, its Therefore, monetary it is not pOssible value through evaluation an estimated. one of the most important outdoor recreational activities in Oregon, estimate a method a to system. market fishing for sport is needed to estimate the value of this important resource. There are several problems existing in the growth of this form of recreation. rise In particular it has given to conflicts in resource use. There is growing competition between the the commercial fishery and the sport fishery. same time there is increasing pressure to use streams purposes for migration and near streams, which would spawning of such fish Timber salmon with interfere At the harvesting hydro power development, flood control, and pollution are seen as potential hazards to the maintenance of salmon runs. One newspaper reported '1One turbine Winchester Dam was shut down Wednesday to divert Thu., migrating fish to ladders." in an attempt (The Oregonian, Aug. 9, 1984). Another concern is the mounting call for funds to increase the fishery stock. salmon has at sport anglers have grown, As the number of more and more been placed upon fishery managers to improve pressure present 5 migration and spawning areas and to invest more money research. Of course, rational decision-making will not be in possible if there are no values available for all kinds of uses. Several Oregon, early studies e.g., Brown, on sport the fishery and Castle (1964), Singh, of Stevens (1966) etc., have enlightened us on this subject. However, by estimating the valuation of fishing only without providing the value estimates for the end products of the fishing, i.e., subsequent the fish caught, these studies has been somewhat limited decision-making generally can purposes. For instance, and earlier public for hatchery stocks withstand far greater harvest than rates natural stocks (Pacific Fishery Management Council, 1982), and hatchery stocks have become large since, the fish Oregon Department of Fish and Wildlife for example, operates hatcheries which produce almost 90 million fish 33 per year (Oregon Blue Book, 1979-1980). However, without value per fish caught, enhancement will a rational economic analysis of not be possible. In addition, fishery these earlier studies effects, i.e., analysis. Consequently, the value of the resources or the benefits have not substitutes considered were the omitted cross-price from their to users may have been incorrect and the implied optimal allocation of resources may have been distorted. To engage in resarch in any field of social science, 6 information pertaining essential. data, No problem matter what methods are used through questionnaire, research the to documentary sources, to is collect observation, mail etc., all social science or interviewing, data are usually uncontrolled or nonexperimental. Even in the the case of a complete enumeration of the population, data may be subject to serious errors due to faults in the methods measurement or observation of (O'Muircheartaigh and Payne ed., 1978). These response errors may arise from the questionnaire, from the execution of the fieldwork, or from nature the of the collection data value response errors are the difference between the true and the value recorded on the schedule. cause The process. These errors will the bias in the estimated regression coefficients, well-known "measurement error" problem (Johnston, 1972). Early research on estimation the outdoor of recreational benefits was based upon average participation rates and travel costs Clawson (1959), (1964). Some researchers, demand in Brown, Singh, and Castle Knetsch (1963), Gum and Martin (1975), gains for various distance zones, e.g., e.g., later suggested that efficiency in estimating functions observations Brown and Nawas (1973), outdoor could be obtained by instead of zone averages. using substantial recreational individual However, in a recent study Brown et al. (1983) argued that if individual observations are to be used, each observation on participation should just the traditional zone as for be adjusted to a per capita average basis, cost travel model. Nevertheless, several criticisms have been advanced concerning the preceding argument. Based analyze upon the above statements, this study and discuss these statements in more will detail and demand, and suggest possible solutions. Objectives The main objectives of this thesis are: To study specification the value link between and and measurement of demand for salmon sport fishing in Oregon. To investigate the sources of error in the salmon sport fishing demand analysis and to use the instrumental variable method to deal with the measurement error. To the demonstrate empirically how different versions of travel cost method can affect the amount of estimated consumer surplus. To analyze and compute average and the marginal values of primary site and substitute sites by and hedonic travel cost methods. using regional Methodology This thesis is concerned with consumer behavior with regard to the salmon sport fishing activity. A basic model of consumer behavior can be formed by including time travel dimensions. Theoretically, this involves and an activity model and a derived model (just as the producer's input demands are derived from the underlying demand for the commodity which he produces, the consumer's demand for outdoor recreational activity demand for travel to it.); economic the can be foundation interpretation for of an empirical the parameters of the there is only an practically, model of the travel demand. by measured This model provides model such permits and an model in the context of an evaluation problem. empirical Therefore, the travel cost demand model will be seen as a key feature of this approach, both because of the importance of the spatial aspect because of the relatively easy collection of travel data. In practice, at the in outdoor recreational activities this approach will be used to observe people the destination and compute their costs of site distance curve. measure and as a function of the decay distance access traveled. function can be translated into a to This demand Moreover, the rate of distance decay is taken as a of the valuation recreational activity itself. placed on the outdoor Basically, employed of the consumer as an evaluation method to measure the salmon sport fishing. above, surplus approach will Following the be benefits demand analysis the demand curves are used to link the willingness to pay with the estimated value of fishing activity. Source of Data A sample population 1977. of This licences anglers drawn was Oregon angling licences sample sold, licences 9,000 of purchased was about 1.5 percent including in-state of all categories. of and the from during total the out-of-state A questionnaire was designed to obtain data from the angler about his expenditures and fishing activities on a quarterly basis. The questionnaire was mailed at the end of each quarter during 1977 first January Quarter, questionnaires were sent; April 1 through June 30; 1 through March 2,700 were sent For the 1,20,0 31, out covering 3,600 questionnaires were mailed for the period July 1 through September 30; and 1,500 were mailed for the October 1 through December 31 quarter. should be different information the noted that the questionnaires were sent sample of anglers for each (It to quarter.) a More was expected from the survey by concentrating bulk of sample in the most active fishing quarter spring and summer. 10 An resulted extensive mail and telephone follow-up a total return of in addition to all non-respondents being telephone to complete and return the respondents suspected whose of telephoned. consuming, was 55o6 about questionnaires percent. In reminded by questionnaires, all incomplete or were being erroneous in some respect Although campaign were also this procedure was costly and time- the quality of the information from the survey greatly improved by the telephone follow-up. detailed information about the survey design, copies of the questionnaire, along More with has been reported by Sorhus, Brown, and Gibbs (1981). Data on the number of salmon caught for each river or port during 1977 were obtained from the Oregon Fish and Wildlife Department. salmon-steelhead To estimate the total annual catch, tag return data were statistical port were 28.44 percent of about returned supplemented checks and creel sampling for 1977. the with There data. salmon-steelhead tags These tag returns have been corrected for nonresponse bias to get an estimate of 372,174 for the total salmon catch by sport anglers in Oregon. Outline for Presentation of Research in this Study Some important theoretical considerations in the specification of demand models for outdoor recreation will 11 be presented considerations, in chapter 2. Following these theoretical site empirical estimates of single some types of travel cost demand models for Oregon salmon sport fishing will be presented in chapter 3. estimates travel will cost include demand several model researchers in the past, specifications have been that Singh, individual (1973), and the used by Castle e.g., Clawson (1959), (1964), observation approach, (2) e.g., unadjusted the Nawas Brown and and Gum and Martin (1975), and (3) the individual observations, adjusted to a per capita basis, (1983). of namely, (1) the traditional zone average model which was first used, Brown, empirical These These three different versions of Brown et a].. cost travel methods, which use aggregated and disaggregated data, will be appraised and discussed in chapter 4. In addition, discussion of the problem of measurement error in reported travel costs and a solution to this problem will be presented in chapter 4. In order to include quality and substitute variables in the model, a regional travel cost model of the demand for fresh-water salmon sport fishing will be estimated and presented in chapter 5. In this chapter, a modification of the travel characteristics also water cost method that incorporates site -- the hedonic travel cost method -- will be discussed and empirically applied to both and ocean salmon sport fishing in Oregon. fresh- Summary 12 and conclusions will be presented in chapter 6. 13 II. SOME THEORETICAL CONSIDERATIONS IN THE SPECIFICATION OF DEMAND FOR OUTDOOR RECREATION In a rational conventional demand theory, will strive to maximize his utility constraint. various purpose of the theory is to explain economics which is concerned with for termed often This is services by consumers. the the theory is i.e., to explain and predict the observed demands and positive what the Another purpose of the theory has economic relations are. been subject to his income factors that affect demand, designed goods One consumer By way of applied to normative problems. contrast, this is termed normative economics which is concerned with what ought be to with set a of criteria for the measurement of "good1' and "bad". Thus, economic policy can be made through judgements, and, such criteria hopefully, the which involve value economic well-being of consumers can be improved. For outdoor recreation the definition and the factors determining demand. with for For demand are much the same as for conventional the consumer's taste is a factor regard to outdoor recreation as it is to the demand any instance, other commodity; the income of individuals similarly has a relation to outdor recreational demands. However, outdoor there recreational are several demands and differences between conventional demands. Many outdoor recreation sites are provided at a zero price or only a nominal entry fee insignificant The entry fees are usually compared to other users' expenses, such as transportation cost. factor alone recreation, would to the be If the entry fees are used as estimate the proximity Therefore, for price factor is in most terms of of demand outdoor locational availability and of substitute outdoor recreation sites may Similarly, accessibility outdoor for most important factors affecting ignored. recreation demand the price relative the be expected to have an effect on the demand. During recreation the has recreational past two decades, research on outdoor started to focus upon the measurement benefits. Conceptual frameworks have of been developed to assign monetary values to outdoor recreation. Therefore, these intangible values. benefits There are are no regarded longer a variety of methods for measuring the benefits of outdoor as estimating recreation, but only a few of them are appropriate and valid. In this chapter, formulation and estimation considerations will be discussed, respectively, from the view of demand for outdoor recreation. A Model of Demand Analysis for Outdoor Recreation Demand is a multivarjate relationship. Many factors, such as price of commodity, consumers' income, consumers' 15 tastes, prices of other related wealth, population, policy, etc., are the particular product. has income can determinants of the demand for model other prices, This simplification of reality help us to understand the consumers' alternatives. way they available among choose thus decision-making In the same manner, an estimation of such a planning demand for outdoor recreation can aid of a But the conventional theory of demand and tastes. processes--the government distribution, emphasized the price of the commodity, income, consumers' commodities, and policy choices by focusing on the important variables. A framework established thus is to the investigate interactions among these important variables. Theoretically, individual's many decision participate to in particular a outdoor recreation activity. Variables such as age, income, be put in and individual education can characteristics; other an affect can factors the sex, category of such as variables, travel cost, congestion, and resource characteristics, are in the category of availability recreation. of Empirically, the number of variables to be included in the model depends upon the nature of the phenomenon being studied and the purpose of the research. In his original demand functions demand schedule for research, four of the Clawson(1959) national was measured by plotting the derived parks. The estimated 16 cost per visit in relation to number of visits per 100,000 population indicated Knetsch (1963) in a distance zone. that C1awsons demand function was underestimated of He also the effect of the time constraint. that other Based variables upon Clawson's method, (1964) the demographic should included. Castle and incorporated income as an independent variable in They claimed demand function for outdoor recreation. that suggested be Singh, Brown, because "the Clawson approach is a special case of the general phenomenon of transfer costs"(ibid., more They p.10). thus could apply these transfer costs to estimate the net economic value of the sport fishery resource. Clawson and Knetsch (1966) used population, leisure, demand multiple a factors the major significant households, affecting Tolley Boyet and regression model to (1966) analyze areas. the They population, and distance from the park explanatory variables. Ranken participation factors in the use of specific park found that income, were as for outdoor recreation. developed causal mobility and income, and Sinden In a survey found (1971) in various outdoor recreational on that activities was related to the income of the household, the proportion of adults, education, average sex, and age of the children, the age, holidays per year of the household have certainly head. These and other similar studies 17 provided some important insights However, since the recreational preferences and behavior. nature demand of different from for explaining for recreation outdoor the demand for somewhat is some commodities, other possible problems need to be delineated. The Specification Problem The first problem is decide to what constitutes the demand for outdoor recreation, to specify the model by which really relationship the how i.e., among variables will be studied. Time has usually been ignored in traditional theory, which implies that the consumer has instantaneous access to all markets, and the consumption is independent of the the time taken to consume. consumption time demand aspects activities are too However, there are some where the access and important to be consumption ignored. For instance, an activity of fishing involves outlays of money and time for traveling and fishing. and income demand must be taken as budget Therefore, constraints for outdoor recreational activities. recreational both time on. the In addition, activities are not the same as the goods on which the traditional consumer demand theory is based, so the be analysis of demand for outdoor recreation cannot tackled in the same way. 18 would It thus appear that in the case recreation, goods, components, and and time, these are travel are components outdoor of main the inputs to the Therefore, production of outdoor recreational activities. a production theory may offer a moresatisfactory approach than demand theory. In fact, as long as the production for outdoor recreation can be established, various inputs can be derived. the demand for the For example, fishing a activity produced and consumed by an angler requires services of necessary fishing a site, for the angler's fishing. and (An angler can purchase or rent the fishing transport himself to the site.) Of course, equipment, activity equipment and time, the his time allocate to there are some other inputs to the production process that are not under the angler's control, such as water quality, fish density, and congestion at the site. The above represents utility the technical function preferences) production outdoor to function possibilities) can (which constitute represents Becker's the (which combine a consumer's approach. In an innovative article, he said "Households will be assumed to combine time and market goods to produce commodities that directly enter their utility (Becker, 1965, specified as (a) p.495). : U = U (Z , 1 ..., Z in Thus, more basic functions." a utility function can be 19 where the are called commodities, Z and each Z has a i production function of the form: (b) = f Z i where (x , T i X i I time a vector is a vector of market goods and T I of i used in producing inputs combination equations of the be can (a) and (b) The commodity. ith used to construct a utility function of the form: (c) U = U (z z ) =U(f, 1 X ; T , 1 f = U (X ) m 1 1 ..., T m Therefore, consumer's be can choice made by maximizing equation (c) and subject to the income and time constraints. In conventional theory, can demand be expressed as a function of those other variables appearing in the constraints to utility. Thus, a demand function for outdoor and recreation could be a function of both own and relative prices for and time. some income, time, recreational goods As mentioned earlier, apart from this approach, other studies provide additional knowledge about the factors determining the dependent variable. These factors, representing individual socio-economic status and family structure, can also be included in the model. However, the ultimate objective of this study is not to develop a detailed model of the determinants of outdoor recreational activities, particular purpose but to emphasize the demand outdoor recreation. In other words, for the main is to show that the spatial factor is the key to 20 understanding the overall demand for outdoor recreation, and the demand for travel is the core of the problem. The Identification Problem The identification problem arises because price quantity of are simultaneously determined by the interaction supply and demand explained data. Working Decades ago, had (1927) the identification problem by using time-series He showed that, period and of time, the in a particular market at a observed price and given data quantity reflect the simultaneous interaction of supply and demand. However, can function Working showed that a demand or supply be identified if we can assume a relatively stable demand and a widely shifting supply or a relatively stable supply and supply and demand shift, function a widely shifting demand. some However, if both in order to identify the demand variables other than price should be included to explain or account for the shift of the demand or supply functions. Basically, a demand model for outdoor recreation is mainly related to forecasting use and estimating of a specific recreational activity. different purposes modeling the distinguished: of demand analysis, for site-specific outdoor However, three based upon approaches recreation area models, benefits can to be site-specific 21 user models, cost and population-specific models. travel model of demand is a site-specific area model assumes that each per feet ly elastic services. In purchase unit The individual recreationist supply curve for the traditional economics, faces specific Site's an individual will a good until his marginal valuation of the last of good exactly equals the price of behavior which of the The good. this marginal value function thus underlies the downward-sloping demand curve. Now, assume the demand curve individuals, but curve moved in a parallel manner (because the more distant constant is horizontal different have to for supply prices all the the at individuals pay higher prices through thehigher travel and other related costs to reach the site.). Working's article thus provides a basis to trace out the statistical demand curve for that site. Therefore, model is the key feature of the that the individual recreationist site-specific confronts a horizontal supply curve, the price at which he consumes is given, and he can consume any quantity at the given price. Accordingly, demand the quantity demanded is determined by the relation of the individual in accordance with his given price for participation. As a consequence, price and quantity words, are with recreation not simultaneously supply can thus specified, be easily determined. the demand estimated. other In for outdoor Hence, the 22 problem of simultaneity and identifications are not issues, at least in the case of this study. Evaluation Methods of Demand for Outdoor Recreation A series recreational validity. of evaluation methods non-priced for resource have been developed and tested Some of these methods, such as the so-called indirect and direct approaches to estimating demand, involved sites where there is no charge (or insignificant entry fee). been made that recreationists and outdoor to an As a consequence, attempts have would pay, given the price conventional Other methods, such as the cost method, the gross expenditures method, derive only to develop proxies which would show the market mechanism. method, have establishing a hypothetical price for access recreational for the gross national product the market value method, do not attempt to the demand curve in order to measure the value of recreation to the recreationists. The following section will briefly discuss these various methods. Comparison of Various Evaluation Methods 1. Cost Method. This method, National Park Service from 1950 to 1957, value employed by the assumes that the of outdoor recreation resource use is equal to the 23 costs involved in developing it. weaknesses in this method (see, 1962). There are several basic for example, Crutchfield, But the most obvious one is that any resources project regardless whether of alternative could be justified (by uses. So recreational this method), have the resources might this method provides no better means of ranking projects. Gross Expenditures Method. used by This method has been travel or agencies. It state fish and wildlife departments, tourism departments, attempts and other related to measure the value of recreation to recreatjonjsts and the both the local area in terms of the total amount spent on recreation by the recreationists. However, if a particular recreational expenditures would still be activity spent on the disappeared, other goods or services, and substitute which would replace the recreational activity. this method tells nothing about the Furthermore,it does not assess the loss in a move from an original pursuit to alternative uses of the expenditures. Gross National Product Method. This method attempts to measure the contribution of recreation to GNP, by assuming that recreation is a factor of production related to production. assume or Obviously, it is not reasonable to recreation as a factor of production. After all, recreation is essentially a consumer good, even though its pursuit may eventually stimulate increases in 24 productivity. Market Value Method. This method attempts to use the market value of fish caught (in the case sport of fishing) or a schedule of charges to represent the market value of the recreation services produced. But in the case of sport fishing, that may or the product is fishing, may inappropriate not be caught. not the Moreover, seems it to use charges at private areas to fish measure the value of recreation at public areas because the market for all outdoor recreation is not a commercial one, and private areas are often affected by the free public areas. Indirect Approaches to Estimating Demand Method. In applied welfare economics, curve plays welfare of normally would 1980). an important role in measuring the the pay pay consumers. a maximum rather than forego it (Henderson and economic consumer that he Quandt, In economics, this maximum amount represents gross for the consumer, consumer is difference called price cost the actual amount paid by the or expenditure, while the between these two amounts is the net benefits. In other words, rather Theoretically, less for a good than the benefits the the downward-sloping demand these net benefits measure "the excess of which (the consumer) would be willing than go without the thing, does pay" (Marshall, consumer 'S surplus. over what he to pay actually 1961, p. 124), which is known as the 25 While the consumer's willingness to pay for goods theoretically is revealed through the outdoor recreational activities are nonmarket for which willingness to pay may not be private market, commodities from measured consumer behavior in the market. Nevertheless, a number of techniques have been developed and applied derive to willingness to pay for outdoor recreation through indirect and direct approaches to estimating demand function. The benefit indirect estimates nonmarket from situations. approaches, cost, approach observed demand consumer behavior in indirect are three various There derive to the household production function, the travel and the hedonic price, outdoor recreational function approach framework recreation (see, 1983). have been used to values. used production 1981, infers household production (1965) household Becker's to estimate the demand for for example, This The evaluate approach Bockstael and has conceptual providing a sound theoretical framework. outdoor McConnell, merit However, for from a practical standpoint it would be more difficult and costly to use for estimation of outdoor recreational demand the other approaches. than (Considering the characteristics of data sources and objectives of this study, the travel cost method will be mainly relied upon, as discussed in later sections.) 6. Direct Approaches to Estimating Demand Method. 26 This approach direct derives questioning willingness to pay. how much One is economic value of individuals with regard to from their It involves asking the recreationists they would be willing to pay for the participate approach demand and in the outdoor recreational to right activity. suffers from its use of hypothetical This questions. of the weaknesses is the fact that willingness to pay governed directly by the recreationists' ability to pay. Another deficiency is that the bidding game used in this approach typical based upon many assumptions is recreationists incorporate fail to the that into their decisions (for example, the bidding game does not consider such factors as probable substitute activities). Also, serious For example, different answer, problem recreationists depending be of bias often give often a occurs. much a upon whether they are asked how much they would willing to pay to retain their recreational activity versus how much they would need to be paid for loss of the activity. Measures of Consumer Welfare "The definition of a measure of economic welfare for the consumer has been one of the most controversial subjects in economics. Unlike the producer's case, ... the criterion of the consumer--utility--is not observable." 27 / (Just, true Hueth and Schmjtz, 1982, p.69). This is especially for nonmarket valuation, (e.g., Bishop and Heberlein, value such as outdoor recreation where the 1979), measures cannot usually be estimated validated by observable market data. Although often U.S. most welfare used in empirical work to measure consumer example, (for the term "consumer surplus" has been Bureau of Outdoor Recreation, 1973; Dwyer, Kelley, and Bowes, 1977, etc.), it has been plagued by a strict assumption: should then be the constant. the marginal utility If this assumption is Marshalljan demand curve, money of unrealistic, which on the computation of consumer surplus is based, does not reflect the relevant valuation, and the concept consumer of surplus becomes imprecise. Hicks consumer has identified and suggested four measures of welfare-- compensating variation (and surplus), equivalent variation (and surplus)-- that differ from Marshallian consumer correct (see Just, surplus and are more Hueth and Schmitz, the theoretically Chapter 6, 1982). The so-called marginal-valuation curve (or Hicksian demand curve) is defined by allowing the presence of the income effect when price changes. In order to maintain a constant real income, the Hicksian demand curve will lie below (or above) the Marshallian demand curve for a price fall rise). The relationships between these two curves (or is 28 illustrated as figure 2.1. In figure (uncompensated) constant, 11 curve and ) demand represents the D(m) demand H (U (compensated) constant. 2.1, income where H (U 22 utility 0 U held is rectangle the (the area x + z) based upon Marshallian curve D(m). 1 Based upon variation compensated curve in income of p cep 0 the to Hicks.ian 1 consumer surplus may be represented by p cfp held is to p , the increase For a fall in price from p 0 in m represent ) where curves Marshallian H (U 11 ) compensating a (area x) can be defined as 1 amount that needs to be reduced after the price fall maintain the consumer as well off as he was before the price reduction. H (U 22 (area Similarly, based upon compensated curve an equivalent variation in income will ) be p dfp 0 x + z + w) which is the amount of income that 1 must given to the consumer instead of price change to leave the consumer Therefore, consumer as well off as he has become with it the change. is clear from the above that the change in surplus resulting from a price fall will be average of the compensated measures. In other words, the the uncompensated demand curve is a special case which assumes marginal utility of income is the same at different income levels. Thus, if a Marshalijan demand curve is established for measuring economic welfare, its usefulness will depend on the extend to which income variations alter valuations. In fact, as long as the income effect is zero, the 29 price * p p 0 p 1 q quantity q 0 1 Fig. 2.1 The relationships between Marshallian and Hicksian demand curves when price changes. 30 Marshalijan coincide demand curve and Iiicicsian demand curve with each other and the Marshallian measure will and the compensated measures will be the same. However, Hicks indicated that "... So long as the proportion of income initially spent upon (commodity) X is small, the the income effect is likely to be quite small. demand for a single commodity (in the ordinary sense) by consumer whose consumption reasonably is diversified-- it is fair to expect that the main effect of a price-change will be the substitution effect, income Along effect the defended curves will be relatively small." same lines, Willig (1976) consumer surplus computed from while the (1956, rigorously has ordinary as a reasonably accurate measure by p.65). demand theoretically demonstrating that the difference between consumer surplus and equivalent variation (or compensating variation) insignificant in most applications. This implies that the consumer surplus approach is generally robust, what demand compensated curves demand (ordinary demand curve curve) are used is to no matter or Hicksian derive consumer surplus. Thus, consumer surplus may usually be a very good approximation to the appropriate welfare measure. The Travel Cost Method Among the indirect recreation valuation techniques, 31 the travel cost method is most representative and has been used for a quarter of century. suggested by Hotelling (1949) in a letter to the Director of the National Park Service. possible estimate to surplus distance zones essentially He stated that it should be demand based (1959), consumers' upon concentric This method around the parks. applied and functions national parks the for Clawson first was method This to outdoor recreation Brown, Singh, and Castle then valuation (1964), was by and Knetsch (1963, 1964). The spatial aspect is important in the travel method, since origin, recognize that they must get to the the individuals, from different points of site to use the service of the site. the service proxy for capita Thus, recreational the price for will vary according to the travel costs of access to the site. price, demand cost and time To use the travel Costs as a this method involves estimating a function per participation rates as average costs to the site and other socio- capita demand on function of economic factors. function for a recreation site, Based upon the per a the consumer surplus for the site can be computed. As mentioned in the previous section, surplus the consumer is defined as the area under the demand curve and above the price line. For the travel cost approach, the differential costs associated with the use of a particular 32 recreation various site by recreationists, distance from surrogate for price. live who have been the site, Therefore, originally located at farther away, the former and as a those recreationists who closely to the recreation site pay less live used those than enjoy ones a consumer surplus over the latter. In reality, the consumer surplus per capita. is computed by subtracting the amount per distance zone from the actual amount that the travel cost maximum hypothetically would have been paid. spite In method of being commonly used, suffers from several resulting weaknesses. weaknesses Th rigorous from this method involves a number of assumptions. One needed assumption is that the recreationists' response to an increase in user fees would be the same as their response to an increased travel cost of the same amount. assumed to recreation that Secondly, the costs of be incurred solely for participating at the particular site. all travel people in the Finally, population characteristics and preferences. have it in are the assumes same the To overcome the rigidity of these assumptions, several attempts have been made, for example, (1976), sites, to to changes time by Burt and Brewer (1971), Cesario and Knetsch generalize the travel cost techniques to many price incorporate the substitution effects of into the model, and to include a surrogate costs as well as money cost in the analysis, for and so 33 on. Early Oregon studies have used for evaluating the sport fishery the travel with method cost in some modifications, e. g., Brown, Singh, and Castle (1964), and Stevens (1966). Oregon salmon-steelbead Hotelling-Clawson In and Brown, Singh, and Castle's work on the expanded fishery variables. model to include additional addition to the price variable they included on the number of angler days spent on sport distance variable function in a negative fashion, has travel. theory experience Oregon acted as a shifter fishing. expanded indicating that time including the Hotelling's quality of costs concentric the sport fishin9. He defined quality angler success per unit of effort. of of zone recreational as an important determinant of the demand ocean The demand the of an effect over and above the money Stevens by distance They found that income had a positive effect income. travel basic the as for the 34 III. EMPIRICAL ESTIMATES OF SINGLE SITE TYPES OF TRAVEL COST DEMAND FOR OREGON SALMON ANGLING As indicated in the previous chapter, demand for recreation is not sites estimation of the as same the traditional methods of estimating the demand for goods and services will value adopt chapter This exchanged in an organized market. the travel cost method to measure demand recreational the for fishing in Both Oregon. aggregated and disaggregated models will be used, comparisons and but the of their results will not be discussed until the next chapter The travel main objective of this chapter is cost estimates models of the fishing in Oregon catch will so as to obtain the to estimate most accurate demand for and value of In addition, be estimated, salmon the value of the based upon estimates of from the from he Oregon Department of Fish and Wildlife. travel cost model and estimates of fish sport salmon value catch Estimated Zone Average Travel Cost Demand Traditionally, estimate the statistically per the capita travel cost method is demand function used by fitting the relationship between trips per unit population by certain distance zone and the average to of costs of reaching the recreational site from that distance zone 35 Trips the per unit of population can be computed by number of trips to the Site from the summing distance given zone and then dividing by the total population of the same distance zone. computed by averaging the total amount of opportunity cost recreatjonjst distance The average cost per distance zone can be time travel of monetary individual each incurs to reach the site from the zone origin. and original Other socio-economic variables are certainly important for constructing demand functions, but variables such as income, age, or education are difficult to use in an aggregated model. However, average income and average salmon fishing equipment tested in the various models. variables expenditures In addition, be will several dummy are also used in the fresh-water salmon fishing demand model. In this section, the demand for fresh-water salmon and ocean salmon will be estimated, respectively. Fresh-Water Salmon Sport Fishing Among the the various zonal travel cost models following semi-log form was judged to be fitted, the most appropriate, based upon statistical considerations, such as t values, goodness of fit, theoretical coefficients, income considerations, etc., and upon logical and such as expected reasonableness of projections, variable was deleted due to the signs etc.. of (The insignificant t 36 value. Also, deletion of the income variable had very little effect upon the crucial travel cost coefficient, as can be seen from equation (A-i), APPENDIX F.) ln(TRPSCAP) (1) + 0.0001552 = -1.4250 - 0.05024 RTC ii ii (-9.38) SSFE - 1.102 x (2.47) - 1.651 X - 0.9204 X 3 2 1 (-6.33) (-3.41) (-3.81) 2 n = 37 In equation (1), TRPSCAP = 0.816. salmon denotes average '3 fishing trips per capita from distance zone specified river j. RTC combines ordinary operating time. (The third of the wage rate, dividing variable (the with the opportunity average cost of incurred travel of one- and the wage rate is computed by yearly income equipment in zone i. SSFE 2,000.) by the average replacement value of related the cost opportunity cost is assumed to be worth the denotes cost a vehicle plus food and lodging costs travelling) to i denotes revised travel cost which travel while and R 1J fishing salmon The dummy variable X 1 takes one the value of one if the anglers of zone i the Portland metropolitan counties of of Washington, X and X 2 in Multnomah, or Clackamas and the value of zero otherwise. are also dummy variables representing the Rogue 3 and Coos Rivers, one, live and parentheses is respectively, when the value is equal to otherwise represent equal to zero. the t-value. The The numbers in thirty-seven 37 distance zones were constructed from individual 158 respondents who fished in the nine specified rivers. Subtracting distance would zone the actual amount of travel hypothetically in angler the from the maximum amount that j. cost be willing to pay is equivalent to The computing the consumer surplus per capita for zone i. total consumer surplus is then computed by multiplying the per capita distance population consumer surplus by the each in and then summing the consumer surplus zone for each zone. The net benefits per capita for distance zone i can be expressed as a mathematical form: tc 0 (la) CS = :i. /tc i we assume the travel cost demand function has bx form as q = a e i, where q denotes the If semi-log i predicted per distance capita zone and x i i rate participation of denotes the travel cost, the ith while the 1 constant is assumed to include the effect of any other a i variables. tc, then q 1 integral the observed travel cost of zone i by btc = a e i and the consumer surplus is the Denote i i of the demand function as x i ranges from tc infinity. (For a linear form, the range is from tc maximum amount of travel cost, to 1 which causes q to the to equal 1 zero.) zone is: Thus, the consumer surplus per capita in the ith 38 bx (ib) Cs i = ae idx= i ( I Itc I Therefore, btc 1) tc ae 1 btc i -b the consumer computed from equation (1), predicted -b surplus population, the ith distance zone is consumer equal the to the zone the total consumer surplus for each zone Adding up the zonal i Then, multiplying surplus for each zone by consumer total estimated net economic benefit the easily be fishing trips to river j per capita for zone capita obtained. can that is, the consumer surplus divided by the travel cost coefficient. per b 1 b for j tc (O-e capita ibdx =_Le a e i 1 per .bx bx surpluses, is the is obtained. This is traditional approach for evaluating consumer Surplus. Another way to evaluate consumer surplus is the Gum-Martin approach (Gum and Martin, so-called 1975). Following the same procedure, except for using actual fishing trips per capita of instead surplus total the predicted for each river can also figure, be consumer the computed. Estimated net economic benefits to Oregon fresh-water salmon anglers are shown in Table 1 from using equation (1). The estimated catch of salmon in each river reported by Oregon Department of Fish and Wildlife is also included in Table 1. Dividing the traditional and Gum-Martin estimate of 39 Table 1. River Estimated Net Economic Benefits and Catch for Oregon Fresh-Water Salmon Sport Anglers in 1977, Based Upon Zonal Average Participation Rates Per Capita Estimated Catch of Salmon Gum-Martin Traditional Estimates of Estimates of Consumer Surplus Consumer Surplus 193,800 Alsea 2,290 Clacicamas 2,149 487,900 161,900 13,172 1,316,600 1,480,300 573 45,200 45,200 Deschutes 3,833 71,400 87,400 Rogue 8,864 236,600 247,100 Umpqua 4,570 477,100 708,700 14,222 1,720,400 1,638,100 4,692 161,200 160,700 54,365 4,916,300 4,723,200 Columbia Coos Willamette Wilson Total $ 399,900 $ 40 consumer surplus by the total fresh-water salmon trips of 230,280, an average consumer surplus per trip of $21.3 and respectively, $20.5, are obtained. Although an average consumer surplus per fish can be computed by dividing the total estimate of consumer surplus by the number of salmon using caught, decisions affecting justifiably that such "It For example, marginal benefits that decisions making marginal fish abundance and harvest has questioned. is allocation average values for and ... Bishop has argued important are average been for will benefits exaggerate the contribution of recreational fishing at the margin." (1980, p.232) sport The relationships between fishing benefits and fish catch will be discussed in later sect ions Ocean Salmon Sport Fishing The procedure used to fit the travel cost demand model for ocean salmon fishing was essentially the same as for fresh-water salmon except the ports in which anglers went fishing were grouped on a county basis each travel coastal represents a specific-site cost demand model. constructed salmon county from There were 47 the Thus in the distance zones 211 observations that fished for ocean The following equation was the most of several that were fitted: satisfactory 41 = -2.1516 - 0.01745 RTC ln(TRPSCAP) (2) ii ii (-10.86) (-7.38) 2 n47 The symbols r = 0.548. in equation (2) are the same as defined in equation (1). The consumer surplus per capita is computed for each zone, then multiplied by the zone population to obtain the total consumer traditional zones, estimates total a approximately estimate each Summing zone. consumer surplus estimated consumer An for of $15,548,700 of $14,491,700. trip surplus net economic was obtained. surplus was the the for benefit 47 of Gum-Martin The slightly lower at average Gum-Martin consumer surplus per of approximately $57 is estimated by either dividing the total estimate of consumer surplus by total trips 252,950 or by taking the reciprocal of the travel of cost coefficient. Theoretical Relationships Between Angler Benefits and Fish Catch Although the travel cost method for estimating value of sport fishing and hunting activity has long in use, studies making value the usefulness of the earlier have been somewhat limited for purposes and public because those studies have not estimates for the fish caught or the bag the been subsequent decision- provided of game. 42 Consequently, needed estimates of values marginal associated with marginal changes in fish catch or game bag have not been available. certainly total be could Some crude average values obtained by simply dividing estimated the consumer surplus by the total sport harvest of fish or game, but the validity of using such average values has not been justified. However, marginal value importance knowing how of in fish and game abundance changes of crucial the the affect sport fishing and hunting can hardly over- be emphasized. Without this knowledge an efficient allocation of public funds and natural resources instance, salmon fish if sport fishing, expenditures enhance are catch is unlikely. value is unrelated to the then there is no need for For of public on fish hatcheries and stream improvement to salmon runs, concerned. at least so far as angler On the other hand, benefits if there is a positive relationship between salmon catch benefits from salmon sport fishing, and then a strong economic considerable use of public resources to protect and enhance salmon runs can be justified. If consumer a linearly homogeneous relationship surplus and fish catch were found to between exist, it would greatly facilitate evaluation of fishery enhancement projects. it But before proceeding with such an assumption, is important to discuss whether this assumed linearly 43 homogeneous There One relation is consistent with consumer conditions. necessary are two main aspects of the theory. aspect concerns the form of the utility function that would consumer surplus to vary cause fish catch. to The second aspect concerns the kind of budget constraint function, proportionally that would, result in combination with the utility in a particular functional form of the demand for fishing trips. Suppose a utility function is as follows: r r 2q U = q 3. 3 2 b r =bq 1<1.0, Where, 01 2 denotes 1. 0 catch fish 1-r ,q b andb >0, r by anglers, 2 3 denotes q number of 2 fishing trips, and q denotes all other consumption goods 3 This formulation effort the assumes that catch angler has good information about for given rivers subject to approach might and catch-effort then the.situation a household more be the production appropriate, of that but (If catch per unit of effort the angler's control, complicated, unit per is not subject to the angler's control, ratio more also is is function Bockstael and McConnell (1981).) The budget constraint facing the angler is Mpq22+pq 33 Where, M is income, p is the price (i.e. travel cost) per 2 trip, and p is 3 the price vector for other goods. 44 Maximizing (3) multiplier method subject to (4) and using for the solution of Lagrangian the constrained this maximum, a Marshaj.ljan demand function can be derived as: b 2 According for -1 bq iMp 01 2 q (5) to the above demand function, salmon sport fishing trips is a function other of increasing strictly the fish catch expected by words, the demand the angler. In the demand relation in (5) implies that no fishing trips would be taken at all if the angler does riot consider that will the probability of catching fish greater than zero. be The consumer surplus computed from (5) can be expressed as: tc tc b 0 b q 1Mtdx = b q Cs = (6) b 01 Ip X 0 lMlnx 01 p 2 where tc is 2 the largest observed travel cost the (or 0 price that reduces quantity demanded to zero) and p is 2 the travel cost incurred by the angler. implies that the consumer proportional to fish catch q surplus The equation (6) would directly be if and only if b = 1.0. Relation of Estimated Angler Benefits to Salmon Catch The previous section has computed consumer for the various rivers, shown in Table 1. surplus based upon a single equation, The traditional estimates of as consumer 45 Surplus for each of the nine rivers in Table 1 was regressed as a linear function of fish catch, procedure then following a similar to that employed by Samples and Bishop (1985): = -58,981 + 100.20 CTCH CS j (-0.32) Since the n = 9 = 0.714. r j (4.18) constant term in (7) is far being from statistically significant and there are some advantages in using term the linearly homogenous form of (7), was deleted, constant the and the regression forced through the origins, yielding 2 = 94.05 CTCH CS j to = 0.710. r j (6.84) According n = 9 equation (8), the marginal value of salmon catch is about $94 per fish. However, since only the fishing rivers are nine most important salmon represented in Table 1, some adjustments of this value are needed. one, To the degree linear regression model was transformed to double-log Thus, check to see if (8) is homogeneous of form the and fitted to the same data in Table double-log equation was estimated as the 1. the following: 2 1nCS = 5.477 + 0.8594 1nCTCH j n = 9 r = 0.562. j (2.05) (2.69) In order to test whether the degree of homogenity is equal to one, the coefficient of 1nCTCH minus J one is 46 divided by the standard error of this coefficient, and the t-value falls obtained was -0.44. short of Since this small value of significance even at the t percent 50 probability level, the hypothesis that the salmon anglers' consumer surplus is a linearly homogeneous function of is fish catch cannot be rejected. that One important aspect of the preceding analysis the estimated fish completely consumer catch surplus in Table 1. 1 are estimate the Table in independent of the data used to collected Salmon sport catch data are each year by the Oregon Department of Fish Wildlife and are based upon salmon-steelhead returns and surplus analysis other information. based is used However, upon survey steelhead sport anglers in 1977. data data punch and card consumer the salmon and The independence of the of thus makes the estimated linearly homogeneous relationship more impressive. Equation (8) is homogeneous of degree one means that if the number consumer of fish caught surplus characteristic would also were be doubled, then doubled. of linear homogeneityhas some the This meaningful implications. First, as long as the number of salmon catch can be predicted, Second, then if the consumer surplus can be it is decided to increase angler's estimated. benefits, those factors that affect the number of salmon catch should be improved, e.g.,the water quality or the number 47 of hatcheries. mentioned However, to be is that the salmon catch is also influenced by biological and commercial catch accurately predict assumed affect other one factors, in the ocean. needs that thing such as and sport the cannot one TherefOre, the consumer surplus simply from also salmon catch since many other variables can the number fish of caught. Similarly, an merely doubling the number of salmon caught by sport anglers on a given stream would not necessarily double benefits to the anglers also since there are many other variables influence the consumer value per surplus. that could Nevertheless, fish from the above analysis should be the quite useful as an approximation. The Gum-Martin procedure estimate to consumer surplus, which involves using the observed number of trips per capita rather than the predicted number of trips per capita, has some advantages over the traditional approach. The reason is that the Gum-Martin procedure should be less sensitive possible to specification that might errors cause fishing rivers to be over or underestimated. same procedure, surplus the Gum-Martin trips Thus, estimate in Table 1 is regressed as a linear fish catch: (10) GMCS j = -148,728+ 111.50 CTCH (-0.89) (5.09) j model demand the in n = 9 of some following the of consumer function of 48 Again, as for equation (7), the constant term (10) is not statistically significant with a t value than one. in less Since there are some advantages to the linearly homogeneous form again was the constant term of (10), deleted, yielding: 2 GMCS = 96.01 CTCH j (7.29) = 9 j r = 0.763. The hypothesis that the degree of homogeneity of the consumer surplus-fish catch relationship is not equal to one was tested by fitting a double-log function: 2 1nGMCS = 4.0326 j (1.88) Computing hypothesis linearly (3.98) j n 9 (1.0178 - 1.o)/o.2556 = t salmon that homogeneous rejected. 1.0178 1nCTCH anglers' = the 0.07, are benefits net function of fish = 0.694. r cannot catch be The total consumer surplus from the traditional method and fairly close. Gum-Martin method in Table the However, are 1 both in checking the consumer surplus for each river, there is a considerable difference between these two methods. observed the fishing trips to estimate the consumer consumer this method surplus for each distance zone may be more accurate method. Therefore, Martin estimates performs Because the Gum-Martin method uses the equation of than (11), consumer the based In fact, upon traditional which uses the surplus, better than equation (8). surplus, Gum- statiâtically if we use 49 individual observations (instead of zonal Gum-Martin did in their original article (Gum and Martin, 1975), averages), then the statistical difference between these methods these will two methods based upon relationship shown in be more prominent. The comparison the linearly as two between homogeneous of consumer surplus-fish catch will also the section that discusses adjusted be individual travel cost demand. Effect of Other Factors Upon Estimated Benefits Per Fish Many factors, congestion, It had such as scenery, could affect consumer surplus per fish catch. been Metropolitan suggested that proximity area might also be an affecting the level of angler benefits that to the have and correspondingly higher estimates of surplus per fish catch. the factor The hypothesis is demands to Portland important salmon rivers closer to Portland would measuring and access, higher consumer This hypothesis can be tested the approximate minimum distance of each Portland Metropolitan area, assumed to be at least 10 miles. with Thus, all 1y river distances for the rivers in the same order as presented in Table 1, distances in miles from Portland are 104, 18, 10, 212, 65, 245, 172, 10, and 38, respectively. Then, various models for the consumer surplus per 50 river as a function of two independent variables, catch and distance from Portland, traditional surplus river measure of consumer were fitted. surplus, salmon the For consumer the per river is regressed against salmon catch per (CTCH) and salmon catch per river distance times from Portland (DP) in miles: (13) Cs = 112.01 CTCH j j - 0.3224 (CTCH*DP) (9.21) From j 2 R n = 9 (-2.73) equation (13) it could be inferred additional mile from the Port'i/n = 0.860. each that Metropolitan area would reduce the cents. This estimate of the distance from Portland effect actually average value per salmon caught by seems too high since a distance of about 200 miles the would reduce the value per fish to less than one-half value of a fish caught near Portland. distance because from Portland effect may be 32 One reason that the overestimated some of the southern Oregon rivers, such as is the Rogue, almost certainly had a large number of anglers from California. travel It is very difficult to properly estimate the model when a few recreationists cost distance are included in the analysis. of state travel cost equations, estimation if out of and no estimate of the out of anglers' consumer surplus is included in Therefore, great Consequently, state anglers were not included in the the from Table 1. there are significantly higher percentages of out of state anglers fishing in the Rogue and the other 51 Southern Oregon rivers, equation (13) would overstate the negative effect of distance from Portland upon the average value per fish. For the Gum-Martin estimate of consumer surplus, the same procedure was used as for (13) yielding: GMCS (14) = 112.55 CTCH j - 0.2969 (cTCH*Dp) j j (9.30) (-2.53) 2 n R 9 = 0.876. Result from (14) are similar to those from (13) with an implied reduction in value per fish of about 30 for each area. additional mile from the Portland It distance should statistically Metropolitan be noted that the coefficient from Portland variable, DP, cents for the by itself was not significant for either the traditional the Gum-Martin estimate of consumer surplus, or although the DP coefficient did have the expected negative sign. The or estimate of consumer surplus per fish from (13) has (14) approximation, for salmon relatively of to be given considered as rough very a the fact that the consumer surplus fishing on the southern Oregon stream may underestimated because of a larger California anglers. Furthermore, some be percentage anglers may prefer chinook salmon over coho, and total salmon catch of all species cannot reflect such preferences. although salmon, the anglers in this study fished a stream that offers a higher In addition, primarily for probability of 52 catching both preferred. creel salmon and steelhead have might been In order to investigate some of these factors, survey data from the Oregon Department of Fish and Wildlife will be examined. Since of creel census data are not available for the rivers in Table 1, most two the analysis will include rivers only. It is believed that the creel surveys provide more Table accurate 1 steelhead much estimates of catch than the catch data which are based primarily upon tag returns. and salmon the These creel surveys also in provide more accurate data on effort than this study used to estimate consumer surplus as shown in Table 1. For the Deschutes river, that the 1977 creel census data indicate catch of adult spring and salmon was only 1,459 adults and 915 jacks. catch chinook fall estimated from salmon and steelhead tags was as shown in Table 1. the However, 3,833 In addition, salmon fishing trips on the Deschutes river were apparently underestimated by relatively small 1977 survey of Oregon anglers, the resulting in too low estimates of consumer surplus in Table 1. Given the seems per 1977 creel census data for the Deschutes river, that a more realistic estimate of consumer fish could be computed by dividing the it surplus Gum-Martin estimate of consumer surplus in Table 1 by an adult salmon equivalent (Assuming catch three based upon the 1977 creel census jacks would be equivalent to one data. adult 53 salmon, an adult equivalent catch would be 1,459 + (915/3) = 1,764 ) Thus, a somewhat more accurate estimate of value per salmon catch 1,764 on the Deschutes river would be = $50 per fish, underestimate $87,400 although still too low due to of salmon fishing trips for the / the Deschutes river. For catch the Alsea river, of creel census data indicate 283 adult chinook and 785 jack chinook adult coho and 185 coho jacks. data are far and These more accurate below the 2,290 salmon used 96 catch Table in a 1. However, it appears that the overestimate of catch used in Table is at least overestimate of effort reulting a 1 in partially from offset the corresponding 1977 by a similar angler survey, overestimate consumer of surplus for the Alsea river in Table 1. Although sources the comparison between data different cannot be scrutinized in more detail, thing one that can be concluded is that most of the variation in the value per error, catch both catch If due to sampling in the consumer surplusby river and in estimates returns. the fish by river in Table 1 is based upon salmon and steelhead the tag creel survey data were available for most of rivers then both the consumer surplus and the estimates could be corrected to give more values per fish by river. Of course, salmon accurate other factors that 54 affect the estimated investigated. further But value this per fish also need study does not attempt to be take to steps in this direction due to the limitation of data sources. Estimated Adjusted Individual Travel Cost Demand The zone average travel cost method (originally employed by Clawson (1959) and followed by Knetsch (1963), Brown, Singh, and Castle (1964), and others) was criticized as being inefficient, due to the potential loss of information from averaging within distance zones (Brown and Nawas, recently, 1973; Gum and Martin (1975). Brown et al. observations are (1983) argued that if to be used, more However, individual each individual dependent variable observation should be divided by its share of the population trips and expressed as trips per capita only, expected not the different distant zones to have quite different reasoning are since instead population can of be The sizes. is that if the individuals' participation rates adjusted to a per capita basis, then a biased estimate of the travel cost coefficient can result because the procedure would not properly account for cases where a lower percentage of the people in the more distant participate in the particular recreational zones activity. In the next section, the individual observation adjusted to a 55 per capita basis will be Following discussed. that section, the individual observation itself, the unadjusted individual observation, will also be discussed. With the the adjusted individual observation number observation factor, of salmon fishing trips for each is first multiplied by the sample then distance zone. individual divided For expanded example, there suppose from one distance expansion are zone to represent 500 salmon angling trips, to its five with Then, if the first observation were would be divided by its share of populationi 5,000, individual by its share of population in observations population of 25,000. approach, this 500 25,000 1 5 = give a per capita participation rate of 500 / 5,000 = 0.1. Fresh-Water Salmon Sport Fishin9 Following the above procedure, a total of 158 individual observations were used to obtain 158 individual participation rates per capita. ( For'the zonal average approach, these 158 observations were used to construct 37 average participation rates per capita, as shown in first section model was one of the better models fitted of the in this chapter.) The following individual travel cost demand functions: the semi-log various 56 (15) ln(TRPSCAP)ij = -2.693 - 0.02175 RTC1j + (-4.44) 0.00004939 SSFE (2.19) n = 158 equation less than counterpart model, (15), one-half in R = 0.131. the travel cost coefficient absolute magnitude in the traditional zone average is of its travel cost equation (1). This smaller travel cost coefficient implies a value per trip of nearly $46, which is more than twice that estimated from equation (1). equation amount (15) that there likely was is error of in the travel costs considerable a reported respondents in the 1977 Oregon anglers survey, when some trips receiving the measurement were made two or questionnaire. error, three Despite this than the by especially months before problem of the estimates of consumer surplus for nine rivers were computed from equation (15), Table 2. with One problem as shown in The total consumer surpluses in Table 2 are more twice those of Table 1, which were less than $5 million. The consumer surplus by river in Table 2 was also fitted as a linearly homogeneous function of salmon catch. For traditional following homogeneous estimates of consumer surplus, equations (16) and (17) represent the function and double-log the linearly function, 57 Table 2. Estimated Net Economic Benefits and Catch for Oregon Fresh-Water Salmon Sport Anglers in 1977, Based Upon Individual Participation Rates Per Cap it a River Estimated Catch of Salmon Alsea 2,290 Clackamas Gum-Martin Traditional Estimates of Estimates of Consumer Surplus Consumer Surplus 498,000 459,800 2,149 1,493,400 553, 300 13,172 3,896,500 3,347,300 573 190,600 78, 900 Deschutes 3,833 111,400 208,900 Rogue 8,864 641,600 557, 200 Umpqua 4,570 710,700 1,511, 500 14,222 3,255,000 3,980,100 Wilson 4,692 123,000 383,000 Total 54,365 10,920,300 11,080,000 Columbia Coos Willamette $ 58 respectively. 2 (16) Cs = 214.54 CTCH j n 9 = 0.674. r j (6.08) lnCS = 7.1586 + 0.7387 1nCTCH (2.10) Since -0.64, the n= 9 = 0.320. r j j (1.82) the t-value is equal to (0.739-1.0) / 0.407 = Hence, the hypothesis that it is not significant. coefficient equals one cannot be Gum-Martin rejected. estimates of consumer surplus, For the following the two equations were obtained: 2 GMC5 = 224.905 CTCH n = 9 = 0.764. r j j (7. 32) 2 1nGMCS = 4.5849 + 1.0537 CTCH j n= 9 = 0.705. r j (2.12) (4.09) Again, the t-value for testing whether the degree of homogeneity 0.209; is therefore, homogeneity mentioned is 0.258 equal to one is (1.054 - 1.0) / = the null hypothesis that the degree of equal to one earlier in the third cannot section, be rejected. the As Gum-Martin approach for estimating consumer surplus for each distance zone Here, may be more accurate than the traditional the equations (18) and (19) show approach. a better statistical performance than equations (16) and (17). 59 Ocean Salmon Sport Fishing There were 211 individual observations used to generate 211 individual participation rates per capita, as compared capita to only 47 zone average participation rates per Fitting the data to the the earlier section. in semi-log model for ocean salmon the angling, following demand equation is obtained: ln(TRPSCAP) ii = -2.836 -0.01153 RTC + ii (-9.25) 0.00006909 SSFE ii (3.62) 2 n = 211 When fishing the variable SSFE, and related steelbead fishing, R the replacement equipment was deleted, = 0.327. used value salmon for of and then the demand equation was the following: ln(TRPSCAP) - ii = -2.6910 - 0.01169 RTC (-9.12) 2 211 r = 0.285. Equation (21) thus can be compared with equation (2) that was based upon the zone average approach. Just as for fresh-water fishing, the absolute value of the travel cost coefficient in (21) is smaller than the absolute magnitude of the travel cost coefficient for the zone average model of equation (2). This smaller absolute value implies 60 higher net Based economic benefits for ocean the traditional and Gum-Martin upon equation (21), estimates of consumer anglers. salmon surplus were and $19,624,900 $21,647,400, respectively. An average Gum-Martin consumer surplus trip of approximately $86 either the per computed by dividing the total Gum-Martin consumer surplus by total ocean was salmon fishing trips of 252,950 or by taking the reciprocal of the travel cost coefficient (i.e. 1 / 0.01169). One limitation of benefit estimates based the upon (21) arises because of measurement error bias in travel cost coefficient, the preceding However, section for the same reason mentioned in for fresh-water angling. salmon a discussion of the pros and cons of the various estimates will be presented later in the next chapter. Estimated Unadjusted Individual Travel Cost Demand With the unadjusted individual observation approach, each individual observation is utilized in the regression without adjusting them to a per capita basis. for using defended Two reasons by its advocates. they think First, often are unadjusted individual observations averaging eliminates much of the natural variation in the data, thus providing a statistical misleading precision. appearance (It has of improvement been questioned as in to 2 whether R is a satisfactory yardstick of performance. 61 See, for example, questioned 1974.) Vicicerman, they Second, are the validity of assuming observed anglers representative of the entire population from whence came dividing -- i.e., of trips number by they total the population of the zone. Fresh-Water Salmon Sport Fishing The unadjusted observations procedure uses data points and regresses as adjusting the dependent variable. following each 158 the of without them Using this method, the better semi-log model was chosen as one of the models: (22) ln(TRPS) + 0.00010 SSFE = 1.17 - 0.011 RTC j j j (11.68) (-3.23) (3.09) 2 n = 158 R = 0.110. The dependent variable denotes the observed trips of the independent jth individual variables are fishing the and observation, defined the same as the for earlier sections. It should be noted that in (22) there is only one subscript for each observation. TRPS Hence, 3 indicates person the took number of salmon fishing trips during the three month period in person was contacted, and it is used directly. concept zone, of traditional distance the jth which the Thus, the which has been used travel cost method, in has not been adopted the by 62 the unadjusted individual approach. All the of statistically estimated coefficients but significant, in magnitudes the coefficients vary from previous estimates. surplus trip is valued at $61 using the method per and $91 using the Gum-Martin (22) are of the consumer The traditional while the total estimates of consumer surplus are approximately $14 million and $21 million, method, respectively. The net economic benefits computed from (22) are much higher than from (1) and the Brown, (15). individual's capita et (1983) stated al., that if participation rates is not adjusted to a per then basis, coefficient can biased estimates of the travel result because the procedure would cost not properly account for cases where a lower percentage of the people in the recreational the more distant activity. various However, approaches individual observation individual observation) zones (zone per participate in the detailed discussions of average capita, per and capita, unadjusted will be delayed until the next chapter. The consumer surplus dependent variable and Wildlife as per river was Oregon Department of as the Fish and estimates of salmon catch by each river was used the independent variable to obtain the equations: used following two 63 Cs (23) 304.39 CTCH = = 9 = 0.774. r j j (7. 39 ) 2 ln(CS) (24) = 5.128+ 1.02327 1nCTCH j = 0.705. r j (2.44) To n= 9 test (4.09) he degree of homogeneity for if (23) is equal to one, (24) was used to compute t = (1.02327 - 1.0) / 0.2501 0.O93. = relationship Again, the However, average procedures as salmon the value per fish is than three tines the value per fish zone homogeneous linearly traditional consumer surplus and of catch cannot be rejected. more the model in from Following the same except that the Gum- (8). for (23) and (24), estimated Martin consumer surplus was used, a marginal value of $469 per fish can be obtained. (The Gum-Martin consumer surplus also showed a linearly homogeneous relationship with salmon catch.) Ocean Salmon Sport Fishing Following unadjusted the number explanatory the same procedure as above, individual observations were used of trjs variables. taken as a function the to regress of various The following semi-log model judged to be the most indicative of the data: 211 was 64 ln(TRPS) (25) j =0.7249 - 0.003418 RTC (-4.42) (10.23) j + 0.00006321 SSFE (5.33) 2 fl = 211 = 0.193. R Based upon (2), an average consumer surplus of $217 and per trip was calculated using the traditional method, an average value o $293 per trip was computed using by The total estimates of consumer surplus using the tiaditiona1 and the Gum-Martin approach the are Gum-Martin around estimates $55 method. and of million, These respectively. are highr than those estimates using the other estimating approach. and $74 Since the "true" values are unknown there are differences of opinion about the evaluation the various benefit estimates, it was decided to present an eva1uatin of the various estimates in the next chapter. has been recognized that measurement errors It an important problem in estimating the travel cost model. In errors, especially discussed. than the next chapter, Also, traditional discussed. in the problem of reported travel are demand measurement cost, will be some modified travel cost methods other trave1 cost method will be briefly 65 IV. DISCUSSION ANDAPPRAISAL OF SEVERAL VERSIONS OF THE TRAVEL COST METHOD Before activity, estimating researchers the must demand for choose a recreational one appropriate evaluation method along various evaluation methods to meet their requirements. such as After an evaluation method, the travel cost metl!od, has been chosen, another question arises. Like most other equivalent economic exercises, the essential question is whether to use an aggregated disaggregated versions and approach In this chapter, of the travel cost method, disaggregate a different based upon aggregate will approaches, the or be and appraised discussed. The travel cost method is an "indirect" method, that is, it does directly about However, the problems. One not depend upon asking their willingness to the pay recreationists or to sell travel, cost method does suffer from several problem encountered with the travel cost method is the long length of time between the recreational trips of the questionnaire, leading to problems of recall error This chapter sometimes and the completion will discuss the problem of measurement errors in reported travel cos1s, and present possible solutions. 66 Individual Oservatjons Versus Zonal Averages The estimatin of outdoor recreational benefits has been traditionally 1ased upon average participation and travel example, Clawson, Castle, one costs for various distance reason laborious to Prais and Aitchison (1954), to use grouped observations is to numerical observations, for (see, 1959, Knetsch, 1963; Brown, Singh, and According 1964). zones rates treatment another reason keep to the individual the of is avoid data the confidential. Besides these two reasons given by Prais and Aitchison, outdoor one even more important reason to estimate the recreation demand from grouped observations is when it is difficult to obtain accurate measurements. However, substantial some gains recreational researchers in efficiency in estimating observations instead of zone and Nawas, 1973; et Gum and Martin, using (Brown More recently, (1983) expressed concern about the use al. unadjusted individual observations. if averages 1975). that outdoor demand functions could be obtained by individual Brown suggested have individual observations are of They have argued that to be each used, observation on participation rates should be adjusted to a per capita variable biased is basis. They stated that if the not adjusted to a per capita basis, estimate of the travel cost coefficient dependent then will be 67 obtained because the procedure would not properly for account the lower percentage of the people who come from more distant zones to participate in the outdoor recreational activity. Nevertheless, several criticisms have been advanced concerning the preceding argument. One criticism was that there is no theoretical reason for expecting a decline percentage participation from the more distant in zones. Furthermore, no empi!rical analysis was presented to show a percentage zones. participation Therefore, investigate ne possible decline from the distant more objective of this section reasons for participation from more distant zones. expecting is declining A second objective is to estimate the impact of increasing distance upon participation to the rates for ocean salmon sport fishing and to assess its effect uppn consumer surplus estimates. A third objective is to show that estimates of demand based upon unadjusted individual observations can be used to properly compute consumer suz plus if such estimates of demand corrected by relationship. be a a distance and participation This correction procedure will be shown reasonable individual separate to of the to a per capita basis or to the alternative to the observations are adjustment traditional zone average travel cost model. 68 Reasons for DeclininH9 Participation Rates possible One percentage more reason participation rates for the population of distant zones'is the following. demand declining explain to individual the If the functions in all distance zones were symmetrically distributed then demand about some population mean only those distributed above with individuals demand functions demand mean the population function, function would participate fzom those zones that were more than the average distance estimation demand of with the Since from the recreational site. individual unadjusted observations would not reflect the declining percentage of participants, an underestimate of cost travel the coefficient will be incurred. clarify To and illustrate the demand functions remarks, Suppose that the true consider the following simple case. individual preceding for a given recreational activity is (26) 6 - l.O PC q i where denotes a + a i i a random "intensity" variable which 1 represents the difference in intensity of preference among the various recreatjonjsts. If E(a ) = 0, then the mean 1 individual demand function would be E(q ) = 6 - 1.0 i TC I is not an error term, but (It is important to note that a 1 rather is a varible that denotes the difference in 69 intensity or strength of demand for recreational activity among discrete various individuals.) Suppose a is a 1 variable takes certain values that are that distributed symmetrically about zero with the following probabilities. E(a ) = (1/16) fl(-4)+4(-2)+6(0)+4(2)+].(4)} = 0 i The variance of a would then be 2 i V(a ) 2 i2 2 +4(2) +1(4) The 2 = (1/16) {l(-4) +4(-2) +6(0) = E(a -0) I 2 = (1/16) {64) } 4 same implied by (27) is the distribution of a 1 as the distribution of the sum that could be obtained from flipping four unbiased coins where a tail would be assigned a value of -1.0 and a head a value of +1.0. Thus, the probability would equal to a sum of -4, a sum of +4. be 1/16 of obtaining four tails and similarly for four heads giving The probability of obtaining three tails and one head equal to a sum of -2 would be 4/16, with the same probability for three heads and one tail, +2. Finally, the giving a sum of probability of obtaining exactly two heads and two tails with zero sum is 6/16. With (26), the assumed true individual demand function of then consider the simplest possible travel cost and distance zone data as shown in Table 3, from generated equations (26) and (27). For distance zone 1, the expected number of trips per recreationist is E(q ) = 6_1.0*1+0 5, 1 but some recreatjonjsts take more and some take less, depending upon their intensity of demand, that is their a 1 70 Table 3. Observations Generated for Three Distance Zones Where the True Individual Demand Functions Are Assumed to Be q =6-1.OTC +a E(a )(1/16) ii i , i {i(-4)4(-2)+6(0)4(2)-i-l(4) } * Main Distance Zone Population Intensity of Demand Average TC per visit (a) (q) i -4 -2 1,600 2 3,200 6,400 0 2 1 1 3 5 7 4 1 9 1 100 1,200 3,000 2,800 900 -4 -2 0 0 2 0 0 4 8 12 8 4 4 4 4 4 4 6 2 -4 -2 7 7 0 7 7 7 0 0 0 4 16 24 16 4 0 2 4 * i 1 1 1 2 3 Number Total Zone Total Mean of Visits # per Visits Respon- of visits per partic- dents ipant capita $ 2 1 3 1 4 6 4 2,400 3,200 1,200 0 0 0 5.0 2.125 0.4375 1,600 1,200 Assuming a random sampling of one percent from the general population and corresponding expansion factor of 100. 71 value. For example, corresponds to a the first line of numbers in Table 3 = -4; per the number of visits hence, 1 participant Note that the = 6-1+(-4) = 1. is equal to q 1 obtained based upon the binomial number of respondents is Since there is only one respondent for a distribution. = 1 total number of visits would be the -4, total number of visits are equal to q (i.e., the 100 number times of 1 respondents and then times the sample blow-up factor). For the second line of numbers in Table 3, corresponding to a 1 -2, = The estimated total number of be 3 times 4 times the expansion factor of = 6-1+(-2) = 3. q 2 visits would 100 equals 1,200. The other numbers were generated in the same way. should It assigned q . be noted that zero would trips to those respondents who have negative be zero or For example, the respondents in the first line of zone 1 2 with a = -4 would have q i would be indicated respondents increase. = 6-4-4 = -2, and zero trips I will by take (Actually, such zero trips as this more Thus, respondents. travel the is one of the driving costs forces behind the travel cost method.) Fitting cost model observation obtained: the data in Table 3 to the based approach, upon the the linear unadjusted following OLS travel individual equation is 72 (29) n = 58 = 5.5521 - 0.5985 TC = 0.501. ii (14.42) (-7.50) Computing the traditional consumer surplus from (29) an average consumer surplus per participating for zone 1, recreatjonjst $20.50 in about $20.50 is of Multiplying obtained. recreationists by the assumed 1,600 participating zone 1 yields an estimated total consumer surplus zone 1 of about $32,800. for Following the same procedure for zone 2 gives $8.33 * 2,200 = $18,326, and $1.55 * 2,000 = $3,100 for zone 3. Thus, a total consumer surplus of about $54,226 from unadjusted the observation individual approach is obtained. = 6- Based upon the assumed true demand function, q 1 l.OTC + a i computed. true the true individual consumer surplus can be , i For the first line of numbers in Table demand function is q = 2 - TC 1 , 3, the represents and it i one actual participant. The consumer surplus is then equal 2 to (1) 1(2 * 1) = 0.5. (The formula for computing the consumer surplus from a linear travel cost demand function 2 can be shown be to CS (q = i ) * 1(2 coefficient )). multiplying the expansion factor of 100, Expanding surplus of $50 is obtained. surplus computing of $1,800 2 for the rest this consumer . cost Similarly, surplus by a true consumer a total for the second line = 4-TC from q travel I consumer obtained is Following the same by procedure i of the lines in Table 3, a total true 73 consumer surplus unadjusted the obtained the Thus, overestimates I consumer surplus by about 42 percent (54,226 1.42). Of that is individual observation approach true 38,200 $38,200 of course, if distances and travel costs are percentage the participation rates the for distant zones decline more rapidly than the case in such more Table 3, then an even greater overestimation of consumer surplus could result from the unadjusted individual observation approach. It is interesting to compare the error in estimating consumer with surplus from the unadjusted individual that from the traditional zone average Using model. the approach travel zone average visits per capita as cost the dependent variable, the following zone average travel cost estimate of the demand function is obtained: (30) =3 = 5.5625 - 0.7604 TC q = 0.978. 1 (10.38) Using surpluses $13,376, (30), (-6.66) the traditional estimate for zone 1, and $243, zone 2, and zone 3, respectively. of consumer are $24,256, Thus, a total consumer surplus of about $37,875 would be estimated by the zone average travel the true cost model, consumer surplus of $38,200. fairly close to In other words, the error of estimation is only about one percent, much better than the 42 percent error in the unadjusted individual observation 74 approach. The results from Table 3 illustrates the fact estimates of individual observation consumer overestimated, percentage surplus approach from can that unadjusted the substantially be when there is a significant decline in the participation rates of the more distant zones. It should be noted that if one can assume that there is no variation the in participants, i e , intensity demand of then the unadjusted = 0 in (26), a the among 1 observation function. approach However, will this assumption may demand true approximate, the very be not realistic since one can always find great variation in the quantities taken by individuals with similar travel costs. Although the above example in Table 3 is enlightening, an empirical analysis by using actual data seems to be needed to obtain a better idea of the actual magnitude that could be incurred by the unadjusted bias of individual observation approach. Effect of Distance UEon Particiation Rate in. Ocean Salmon Fishing It is hypothesized that a larger percentage of the population would participate in ocean salmon sport fishing from nearby population distance would zones and a participate lower from more percentage distant of zones. 75 Thus, the would null hypothesis to be tested is that have no Participation effect rate the upon distance participation is defined as the proportion rate. the of population who actually fished for ocean salmon during the survey year. This participation rate is then fitted by OLS regression as a function of measured round-trip distance from the zone of origin to the ocean port: ln(y (31) ) = -1.9818 - 0.003806 DIST ii (-23.86) (-12.60) 2 n = 211 The r = 0.432. participation rate is denoted by y which is ii computed family observation divided zone. by multiplying the number of anglers in the ijth by by the sample blow up its share of the population in DIST then factor, its distance is the measured round-trip distance from the ii ith family observation's destination port j. city of In equation (31), residence to the the large negative value of t = -12.60 indicates that increasing distance had an extremely strong negative effect on the rate there for ocean salmon fishing. were no It should be other independent variables participation noted that had that significant effect upon participation rate when DIST was ii included in the equation. For example, the income variable had an unexpected negative sign with t = -1.09, salmon-steelhead variable had fishing t = 0.29. equipment No matter replacement which and the value explanatory 76 variables were included in (31), remained DIST only 1J significant with a stable coefficient and distance important by far the most is absolute Thus, it is clear that value of t always greater than 12. measured with factor affecting the participation rate. One obvious decreasing way to with cope problem the participation rates is to adjust the dependent variable by sample the blow up shared and factor population of each individual observation. (Brown et 1983). of this problem from correspondence between Professors William However, developed al., way another to solve G. Brown and Kenneth E. McConnell. They concluded that the probability of whether or not to participate must also be considered if an unadjusted individual observation type of model is to be used. To scrutinize this idea, first denote the expected number of trips per capita, TRPSCAP , as ii TRPSCAP (32) ii ii ii * BLF = (NA where y ii anglers, NA )/NA * TRPS = (y ) ii ij I POP ii , denotes the number of ii times the blow up factor BLF ij by shared , then divided 13 population POP i , .e., the probability of ij participation as defined for equ ation (31); TRPS denotes ii the reported number of trips by the ijth respondent. Since both and TRPS y ii are greatly affected by travel ii or distance, (32) can be further expressed as: (33) TRPSCAP * TRPS = (y ii )/NA ii = f(DIST ) ii ii * g(DIST ). ii costs 77 Therefore, the computation of consumer cannot validly be obtained by integrating TRPS y 1] surplus only when is also a function of distance as shown in (33). 13 To be see if a valid estimate of consumer surplus obtained based upon (32), can individual the unadjusted data is fitted yielding the following linear equation: ) =0.9288 - 0.001318 DIST ln(TRPS 13 13 (11.41) (-4.45) n = 211 r 2 In (34), DIST = 0.087. denotes the two-way distance from ij the ith anglers city of residence to the jth port, while TRPS trips denotes the number of ocean salmon fishing ii reported valid by the ith respondent to the jth port. estimate integrating of the consumer surplus can be product of equations Thus, obtained and (31) by (34), divided by the number of anglers: TRPSCAP * TRPS (y ii ii )/NA ii ii -0.005125 = (0.34889e )/NA ij Integrating trips per equation (35) based upon capita, corresponding the Gum-Martin the observed consumer surplus to each of the 211 individual observations was obtained. Multiplying each individual consumer surplus by its values share summing all these gave a total estimate of consumer surplus of about $13.56 million. cents of the population and per mile (An average reported travel cost of has been used here, based upon 27.5 the 78 following linearly homogeneous function: RTC = 0.2747 DIST ii 211 = 0.817, r ii (30.63) where RTC is defined as revised travel costs.) ii the If effect of distance upon rates is ignored, i.e., participation the term in (32) and (33) if the y ii is deleted approach total and the unadjusted used to estimate consumer is Gum-Martin observation individual surplus, consumer surplus of $52.71 then million is obtained. It is estimates average also interesting to compute and compare of consumer surplus from the traditional the zone travel cost model and the individual observations adjusted to a per capita approach. Fitting the average number of trips per capita per distance zone as a function of measured distance yields ln(TRPSCAP ) = -2.0280 - 0.005452 DIST ij (-9.71) (-7.49) n47 Based upon (37), 2 r an average =0.555. Gum-Martin consumer surplus of about $52 per trip and a total consumer surplus of that about $13.16 million is obtained. the (It should be noted cost per mile is about 28 cents for the zone average travel cost model.) Consumer adjusted surplus can also be computed by using individual observations approach. Fitting the the 79 individual trips per capita as a function measured distance, the following equation is obtained, 1n(TRPSCAP (38) ) = -2.2755 - 0.005161 DIST 1) (-20.01) (-12.48) 2 n = 211 = 0.427. r Based upon (38), a total Gum-Martin consumer surplus of $13.46 million with is estimated, corresponding a estimate of $53 per trip. These four different estimates of consumer are shown in Table 4. are very surplus The last three estimates in Table 4 close to each other, which is an interesting reult considering that different definitions and equations were used for those three estimates. By contrast, however, the unadjusted estimate Martin individual observation approach gave of about four times that of the other three Gumconsumer surplus comparison The estimates. various estimates of consumer surplus as shown in Table has thus consumer several implications. First, surplus based upon individual observations reliable. Second, solely approach the if participation valid consumer observations estimates can must lead to considered be unadjusted Third, incorrect 4 unadjusted the individual then the probability be linked with it to surplus. of the estimate of cannot observation approach should be used, of an estimate using consumer a individual surplus unless they are adjusted to a per capita basis, 80 Table 4. Estimated Consumer Surplus to Ocean Salmon Sport Anglers of Oregon, Based Upon Four Different Methods of Estimation Method of Estimation (1) Estimated (2) Estimated (3) Estimated Total GumConsumer Total TradiMartin Consumer tional ConSurplus Per Surplus Trip from(l) sumer Surplus (Ulo) $ millions $ millions $ Unadjusted Individual Observations Approach, Equation(34) 52.71 38.48 208 UlO Approach with Probability of Participation Rates Included, Equation(35) 13.56 13.52 54 Traditional Zone Average Travel Cost Model, Equation(37) 13.16 14.50 52 13.46 12.35 53 Individual Observations Adjusted to a Per Capita Basis, Equation ( 38) 81 just as for the zone average travel cost if model. However, all there are equal percentages of participation from distance then zones, not individual observations would need to be adjusted. Measurement Errors in Travel Cost Variable As mentioned earlier, estimating one advantage of consumer surplus by using individual observations is there that the is no averaging of the data which would reduce informational content of the basic data set. corresponding disadvantage However, using of individual observations is that if there is appreciable error in the reported travel costs, then a bias in the estimated travel will coefficient cost "measurement be error" problem caused, (Kmenta, the well-known 1971, pp.3O7-322; Johnston, 1972, pp.281-291). On the other hand, the averaging together of several observations one is method that can associated with measurement error. using aggregate averaged out, reduced and estimate should data, reduce The reason is that in which the wide variations the variance due to measurement the the resulting travel cost error by are is coefficient have much less bias than from using individual observations (Brown, bias the et al., 1983). Therefore, though the zone average method does not have the advantage 82 of disaggregated models in being able to investigate the actual behavioral patterns of individuals, it does help to mitigate the bias from measurement errors. section This measurement empirical will show the effects of comparing errors existing in travel costs by the results based upon different methods of estimation and from the use of the instrumental variable method to solve this problem. Sources and Consequences of Measurement Errors There are two possible sources of measurement errors in the travel cost demand model: dependent variable, i.e., the the one source is from number of recreational trips; the other source is from the explanatory variables, i.e., the it is well known that a random error term However, to the travel costs and other socio-economic factors. dependent variable will not cause a bias regression coefficient estimates. Therefore, important to investigate the measurement errors of costs affects only, the because only the travel consumer surplus cost estimates. added the in it is travel coefficient Travel costs represent a summation of many smaller costs, some of which may not be obvious to the recreationists, such as the wear on tires, and some of these costs are not actually imposed 83 on the recreatjonjsts at the time when the recreation consumed. is several Neuburger (1971) stated that there are reasons why people might fail to correctly consider costs: 1) the costs might be so small that it is not worth taking account of them, 2) certain variable costs may be regarded wrongly as fixed costs, 3) the respondent may be unware of the connection between a particular activity and the costs to which it gives rise. addjtjton In to the above sources measurement of errors for travel costs, it is believed that a substantial error in reporting trip expenses is very likely to list their expenditures spent on fishing trips they which may have been taken two or three months before received their "recall error". very questionnaires. about especially when so-called the is found (In fact, Hiett and Worrall (1977) substantial questioned This recall errors by marine and their fish catch questioned when anglers effort, fishing more than two the were because the respondents 1977 Oregon anglers survey, asked in after months their fishing trip.) there If travel the are errors of measurement in cost variable, then the true error term in the travel cost demand model will not be independent of the variable. following. This Assume statement the can be relationship travel proved between as in the variables is as equation (39) which retains all the cost, the true basic 84 assumptions classical normal the of regression linear model: TRIP =b +b TC +u (39) 0 i where TRIP 1 i 1 denotes participation the rate of ith 1 individual, TC denotes the true travel cost for the ith 1 individual. Suppose instead of using true travel cost TC 1 the observed travel cost tc i where v 1 =TC +v tc (40) I is used: I is a random variable representing the measurement 1 errors in tc The equation with the actual observations . 1 is TRIP =b +b tc +w (41) 0 i where w w = u 1 1 1 a v . Assume u '-s (O,6), v - b ii ii 6w). Also, -'(0, -i_'(O,Gv) and i I assume that the u's, v's, and w's are 1 serially Independent. and w tc i (42) , between To check the relationship their covariance is expressed as I Cov(tc ,w ii ) = E ((tc -E(tc ))(w -E(w ))} i = E((TC +v -TC i i ) I i I 1 w } = E{v (u -b v )} i i 1 ii -b óv 4 0 1 This means that the least squares estimator of b in (41) 1 is inconsistent. Moreover, when there are measurement errors in the travel cost, the estimate of the slope b , i.e., the travel 1 cost coefficient, will have a downward bias. It can easily be shown (e.g., Johnston, 1972, p.282; Koutsoyiannis, 1977, p.263) that the probability limit of b is 1 85 I A (43) plim(b ) = 1 2. 2. 1 + ( 2. where the variance of is measurement and errors, 2. 6 is the variance of the true values of travel cost. 2. Since ( (5y I t5.) > 2. 0, which implies pliin(b < b , ) 1 b OLS the also It measurement zonal cost 6 from by the travel approach used in the traditional This model. to bias foLlows from (43) that the error would be substantially reduced averaging equal consumer causing a corresponding overestimate of surplus. and 1 1 thereby 1 b , underestimates the true coefficient mean is Gv in (43) will be reduced in is because the variance of a 2. In, and hence 2. the zonal average travel cost essentially unchanged. model while 6-ic remains A Therefore, plim(b ) would tend to 1 b for travel cost model with zonal averages as the number 1 of observations per zone average becomes large. The Instrumental Variable Approach From when the that above discussion it should be clear there are measurement errors in the observed travel OLS estimates of the parameters are no longer cost, the unbiased and consistent. generate better estimates should be considered. various Thus, using other methods to Although solutions have been suggested for the problem of 86 measurement errors (see, for example, Koutsoyiannis, 1977, pp. 265-274), a more practical procedure for dealing with this problem is the method of instrumental variables. use of instrumental Reiersol (1941). by developed first variables was The He found that economic variables subject to exact relationship were affected by measurement errors. In an article variables, discussing Sargan findings: use the produce the OLS method is lilcely to 1) may be obtained if measurement reduced somewhat, variables method will produce coefficients even apparent, the 4) use the 3) when instrumental consistent estimates errors measurement large use of large numbers be can errors the of large 2) better biases when there are :Large measurement errors, results useful several suggested (1958) instrumental of of of are instrumental variables may not improve the accuracy of the estimates. Consider simple a model Y a+aX+w = example, where w 1 X and I =u -av due to a I ii as an i dependency between then a procedure to overcome the problem w , of I measurement errors instrumental regression, will be as follows: variable Z x values 0 first, select an i'4.. then use OLS to ; +c Z +e = c i estimated ii o 1 lii ; using finally, from the previous estimate regression, the X , the do OLS A again for the regression, = d +d X +f Y i 0 ii . Theoretically, i the instrumental variable Z should a) be independent of w; b) have a large variance; c) be highly correlated with X; 87 d) have one-way causality relation a used instrumental variable for the as variable (RTc). most appropriate for use in this study. used in different from the above procedure, previous the result were exactly the same. estimating travel cost, Although the was section slightly principle its to and Here, DIST will be used for RTC, then RTC will be used in the travel cost demand function. a cost it is considered procedure as travel Because DIST possesses all the properties desired of an instrumental variable, be the In X. the measured round-trip distance (DIST) previous section, was with Fitting the travel cost function of round-trip distance DIST for the RTC ocean salmon zone average travel cost model 2 = 0 2837 DIST RTC n = 47 r 0.942 i i (27.28) Then, fitting average trips per capita as a function of estimated travel cost RTCS the following semi-log equation is obtained. ln(TRPSCAP) = -2.02803-0.01922 RTC (-9.71) (-7.49) 2 a = 47 Equation r = 0.555. (45) is to be compared with equation (2), the observed travel cost demand equation, for the absolute value of the travel cost coefficient. of The absolute the travel cost coefficient in (2) is indeed lower than in (45), value slightly showing a downward bias due to the 88 the zonal measurement because but the bias is not too large measurement error, average data error, as can alleviate problem the total The earlier. discussed of estimates of consumer surplus based upon (2) and (45) are shown two Table in 5. The difference Gum- based upon the is only about 10 percent, equations these between Martin consumer surplus. was It observations that earlier deduced individual the bias larger is likely to incur a approach than the zone averages approach if measurement errors are existing in the travel costs. Therefore, it is interesting , to fit the estimated travel cost RTC in the adjusted individual observations demand function. RTC was fitted as distance a function of reported (Here, in earlier equation (36)): ln(TRPSCAP) (46) -2.2755-0.01879 RTC ij ij (-20.01) (-12.48) 2 n = 211 Equation (21). of A also = 0.427. then can be compared equation with large difference in the travel cost coefficients two these substantial cost. (46) r equations measurement indicates errors the in the presence observed travel The corresponding estimated consumer surpluses shown consumer in surplus Table 5. between The difference (46) and (21) of are of Gum-Martin is around 61 percent, much higher than the difference between equations 89 Table 5. Variable Used and Equation Estimated Consumer Surplus to Ocean Salmon Anglers of Oregon, Based Upon Observed Travel Cost Variable (TCV) and Its Instrumental Variable (IV), unit: $ million Consumer Surplus Based upon Zone Average Approach Gum-Martin Traditional TCV Equation IV Equation Consumer Surplus Based on Adjusted Individual Method Gum-Martin Traditional 21.65 19.62 (21) (21) 14.49 15.55 (2) (2) 13.16 14.50 13.46 12.35 (45) (45) (46) (46) 90 (45) and (2). In short, based upon the results of observed travel costs are used, are ignored, then the i.e., Gum-Martin Table 5, if measurement errors surplus consumer estimated from adjusted individual observations were about 50 percent higher than the estimate from the zone averages But if measurement errors are considered, i.e., approach. then the difference of the instrumental variable is used, Gum-Martin consumer individual about 2 percent. in observations can is thus clear that results between and adjusted the the was most adjusted of only the individual the zonal average model is due to the from measurement errors in the travel cost variable Furthermore, of It between and the zone averages observations difference bias surplus the difference in consumer surplus from use individual observations per capita versus zone average be variable essentially approach, eliminated using reported travel costs. via the instrumental measured distance in place of 91 V. INCLUSION OF QUALITY VARIABLES IN THE TRAVEL COST MODEL While the traditional single site travel cost model has been widely applied to outdoor recreation, it does not provide the marginal value of a quality change of the site. In addition, this traditional travel cost model does not include substitute sites in the model theory indicates should be included. the Furthermore, without it is almost marginal value for quality of the site, impossible to make critically economic as incremental important decisions. And the consequence of omitting substitutes can result in a biased estimate of the net economic In order to solve these two problems, regional method two methods -- the travel cost method and the hedonic -- will benefits. travel be discussed and applied to estimate cost the demand for salmon sport fishing in Oregon. Using Regional Travel Cost Models To Estimate The Benefits From Fresh-Water Salmon Fishing The travel cost method has been typically applied to estimate the value of the particular sites assuming by that all participants have the same opportunities to reach all substitute sites at the same cost. important assumption, and Based a single site model can be substitutes are thus omitted from the features of upon this formed, analysis. this technique have been criticized by The many 92 appplied this One of the criticisms is that economists. value the for technique only site, does not provide information about the marginal it estimates an all-or-none value of quality changes in that site. The other criticism is that this technique cannot justify whether to develop a new site or not. criticism another addition, In is associated with the omission of substitutes which causes a Therefore, a method biased estimate of economic benefits. for predicting the demand curve for and value of a new changed recreation limitations the site presented next. having above the A construction and discussion is needed. so-called without travel regional cost method or will of be The other method, which uses a multi-site technique, will be presented in a later section. Regional Travel Cost Method Although related to the regional travel cost regional economics, both method is emphasize not the importance of the effect of spatial factors. However, some of the underlying logic of the regional travel cost method coincides with economics. Therefore, the driving it original spatial theory, 1966) model of land use, travel cost method. force behind regional seems plausible to discuss the the von ThUnen (see, e.g., Hall, before presenting the regional 93 Von Thlinen considered the pattern of land use as function of the different prices of agricultural goods and of their different costs of production, market and distance to a center as a significant determinant introducing location independently into economic theory, effect that were measurable. there relevant variables other was By only cost but real-world In order to assess the of distance on systems of production, assumed he not the theory of marginal invented also developed an economic model with specific predictions cost. of constant. no variability in transport cost von He Thiinen assumed except that imposed by distance; he assumed prices to be determined in the market center by the normal operation of demand; supply and and he assumed no barriers to trade or production other than price and cost, and so forth Under these monotonically conditions, transport with distance from the market rises cost center, and transportation is the major variable factor of production. Increasing transport costs have the effect of lowering the farm gate price of any good produced further away from the market center, extra (marginal) inputs of labor and capital in its production Therefore, the lowering the return to rational producers will intensify production near the center and use land less intensively as they live away from the center the travel cost further Similarly, the driving force behind method is that recreationists from 94 different common origins incur diffeient travel cost to reach different can be expected to participate at site a rates. Based data upon the revised travel cost method and and the 1977 angler survey and from the Oregon Fish from Wildlife Department, cost the following regional travel model was specified. TRPSCAP (47) = f( DIST , FISH /DIST ii SSFE , TRPSCAP distance zone denotes ik k INC ii ii where, /DIST , FISH ij j trips per capita from the origin to the jth DIST river; ith the is 13 measured of one way distance from the main concentration population in the ith distance zone to the nearest part of the jth river. Quality of the jth river is approximated by (FISH /DIST ), where ii j j The effect of substitute catch in 1977 for the jth river. sites represented is salmon annual denotes the FISH by ), where river, and (FISH /DIST k FISH k i]c denotes the annual catch of the kth denotes the measured portion of the kth river. DIST 1k all one way distance with largest value for and the nearest selecting (FISH /DIST k denotes the The kth river was chosen among of the possible substitute rivers by river to ). that SSFE ij 1k average replacement value of salmon related equipment in zone i to the jth river. fishing INC 13 represents the average income for ith distance zone to the jth river. 95 The above shows distance function play will an Just as important role in the regional travel cost model. distance triggered the development of von Thunen's thesis, distance travel cost cost distance the key for constructing regional a travel Based upon the theory of the model distance method, negatively has also is related, and fishing implies that which demanded are increasing the trips from the origin to the recreational fishing site trips the effect of lowering the quantity of fishing taken. The coefficient of the quality variable is expected to have a positive sign, expected fishing trips affected by replacement negatively related to be to while the substitute variable is demanded. distance. These two The the quantity coefficients both are variables of average of value of fishing equipment and average income are expected to have a positive sign, according to general economic theory. instrumental It should be noted that distance is variable for travel cost, which will an rise monotonically with distance. demand Equation (47) specifies the trips per capita function this one for the fishing sites in a region. equation, one could estimate the using Thus, particular demand function for any existing recreational fishing site in this region, opportunities no matter whether the have been changed or not. salmon fishing Moreover, this model is a good substitute for the contingent value method 96 to estimate the value of a newly site (or to decide if a new site is worthwhile to fishing develop). fishing opportunities, and and newly proposed although a contingent value it is often too time-consuming.) By including quality and study could be conducted in such a case, expensive travel that the traditional single site (Note method cannot estimate the value of cost recreational developed the substitute variables in a regional travel cost model, value will of fish will vary with site quality and be travel cost model. to the predicted too, trips simply of salmon because Therefore, trip be the quality of the then hatcheries, and economic benef.ts will be improved. can is increased due For example, if FISH enhancement model traditional the theoretically sound than more the fishing increased sites is the marginal value per fish or per course, the derived from this model. Of counteracting effect from an increase of substitute FISH k also can be estimated from this model. Estimation of Regional Travel Cost Demand Model Although several functional forms of regional travel cost models were fitted to the fresh-water salmon fishing data from the 1977 Oregon anglers survey, equation is one of the better results, statistical performance and prediction: the following based upon 97 1n(TRPSCAP) (48) -4.6081-0.02603 = DIST ii (-1.92) (-3.19) 0.075 +1.912 (FIsH /DIST -0.0007109 (FISH /DIST ) ii i (1.32) (-2. 78) 2 R n = 38 In because = 0.448. were the INC and SSFE variables equation (48), included not being both t values' were far from statistically significant Also, the quality variable with of 0.075 had a better t value than with a power power There 1.0. using several other advantanges by are that a smaller sum of the ii j is of . One power of 0.075 for the quality variable, FISH /DIST advantange ) ik Ic squared residuals and another advantange is that a decreasing marginal consumer surplus about the regression can be obtained, per fish results. 1.0 will have an increasing marginal consumer surplus per fish, which However, the it fishing (The quality variable with a power violates the law of diminishing return.) should be noted that the power of 0.075 quality variable is somewhat of for than smaller originally expected. Based upon (48), the consumer surplus for each river computed was total and is presented in Table 6. Dividing the of consumer surplus by the total fresh-water salmon trips Of 230,280, an traditional and Gum-Martin estimates average consumer surplus per trip of $23.8 and respectively, was obtained. $23.7, A marginal consumer surplus 98 Table 6. Estimated Net Economic Benefits for Oregon FreshWater Salmon Sport Anglers in 1977, Based upon Regional Travel Cost Model River Traditional estimates of consumer surplus Gum-Martin estimates of consumer surplus Alsea 129, 300 236,600 Clackamas 529, 300 197, 000 1,701,430 1,637,810 135, 200 54,900 80, 070 107,470 Rogue 431, 320 304, 560 Umpqua 559, 940 790,470 1,856,160 1,929,150 61,900 191, 200 5,484, 620 5,449,160 Co lumbi a Coos Deschutes Willamette Wilson Total 99 per catch fish of $30.9 for a projected increase in fish of 100 in the Columbia river was obtained by assuming that estimates marginal consumer surplus per (e.g., fish in for a projected increase of 3,000in fish catch $27.6 the of Smaller unchanged. catch in other rivers remaining fish larger Columbia river) were obtained for projected increase in fish catch. Using exactly the same variables as in (48) but with a different functional form, the following linear equation was fitted, (49) TRPSCAP 0.007841-0.002433 = DIST ij (-2.53) (0 028) 0.075 +0.1423 (FISH /DIST -0.00009138 (FISH /DIST ) ij j ) k ik fell far (-3.02) (0.831) 2 coefficient The of = 0.342. R = 38 the constant term in (49) of statistical significance with a t value of short 0.028; thus, constant the term was only and deleted the following equation was obtained, (50) TRPSCAP = -0.002415 DIST (-3.47) 0.075 +0.147 (FISH /DIST j - 0.00009149 (FISH /DIST ) k ij (-3.10) (6.87) n38 Although ) ik 2 R =0.342. the magnitude of the coefficients for the 100 explanatory variables in similar are (50) the to coefficients for the corresponding variables in (49), values in (50) are larger. t equal, equation (49). Both consumer being things other Thus, all (50) statistically performed better than and (49) per surplus (50) lower total regional travel slightly but fish marginal diminishing have estimates of consumer surplus than from (48). Other specifications of the above cost model were also fitted by OLS. gave good example, version results t from values for Those equations also viewpoint. statistical a the (Bowes and Loomis, Squares Least Generalized given 1980) of the model For in equation (50) were all significant with absolute values of at least 4.0. Another specification tried was to use total trips, TTRPS , as the dependent variable, rather than ii (49), and (50), with the trips per capita as used in (48), explanatory POP , variables multiplied by the zone population, following The corresponding to that observation. 1J equation for this kind of model was fit by OLS: (51) TTRPS = -0.001443 (DIST*POP) ii (-4.56) 0.075 + 0.09122 (FISH /DIST ) *pp ii j (6.38) - 0.00005637 )*POP (FISH /DIST ik k (-4.71) n38 2 R =0.132. 101 The Gum-Martin estimate of consumer surplus computed from (51) is about $6 9 million which is somewhat than computed from absolute value equation (51) tends to be too small. the value of observations and (Pop) of coefficient the negative values for TTRPS. observations, large that those for population of coefficient forcing the predicting of large For example, one of the actual but the had actual total trips at 9,998, value of total trips was only about coefficient absolute in with large shared population at 295,800 and distance at 63, the (DIST*POP) The reason is be quite small to avoid to predicted the with unusually larger values distance (DIST), (DIST*P0P) of becomes too (DIsT*pop) that It should be noted (48). larger value, of (DIST*P0P) was 10 percent then predicted total the 2,654. If larger in would trips become negative. Furthermore, distributed since around heteroskedasticity population the the probably exists problem the site, unevenly is (Bowes and of Loomis, 1980). If the square root of the population is used as the weighting squares equivalent (Ibid, of factor, then estimates of resulting "the such weighted ordinary least observations to generalized least square (GLS) are estimates." p.468). But population rather than the square root population was used in (51), this population factor thus resulted in another kind of heteroskedasticity. Since 102 none of cost the above specifications of the regional travel all other model clearly seemed specifications, superior to based upon statistical considerations and reasonableness of estimated net economic benefits, the Box and Cox transformation procedure (Zarembka, useful be 1974) may for the choice between different functional forms. However, the procedure of choice of a functional form will not be presented in this study. One noteworthy from interesting result and this study was that the fishing quality variable, FISH /DIST ii always had more explanatory power when assigned a power of 0 075. This unexpectedly low value may data. In specifying the model, has be caused primarily by poor specification been included explanatory related avoided, then is only one quality variable not a appropriate very If fish density and other quality- variable information available, may which and for each fishing specification this or at least mitigated. stream problem This poor could were be specification also explain why the marginal value per fish was only about case 25 percent of the average value per fish of the Columbia River) (Similarly, the (in the marginal values per fish were only about 25, 20, 40, and 20 percent of the average values per fish for the Willamette, Utnpqua, Rogue, and Deschutes rivers, data used in this model, respectively.) As for the recall errors by the respondents 103 in the 1977 returned Oregon angler survey and the salmon-steelhead are tags rate low probably promising cost fairly results were obtained from the regional analysis. values possible by travel more accurate estimates of per fish for specified streams might be Furthermore, marginal main the causes of inaccuracies in the data. Nevertheless, of combining the steelhead data from the 1977 angler survey angling data (since there were almost twice as many observations from with the fresh-water salmon the steelhead anglers). similarly, it might be possible to include the ocean salmon angling data with the fresh-water salmon an in extended regional travel cost analysis. However, such an extended analysis would require resources beyond those available for the completion this of dissertation. Use of the Hedonic Travel Cost Model to Vaule of Site Characteristics Estimate Since Hotelling-Clawson's travel cost method the yields only the value of a given site in its current state, it is not helpful in choosing between options that change the sites' recreational characteristics. Although the regional travel cost method resolved this problem in a usefulness limited. model, and The completeness are somewhat sense, its theoretically reason is that in the regional travel cost it is doubtful that changes in characteristics can 104 be related clearly to anglers' utility and welfare. In cost the next section, a modification of the travel method incorporates site characteristics to yield hedonic travel cost method, which will be discussed a and. empirically applied to Oregon salmon sport fishing. This method a based upon has sound theoretical framework techniques used by Lancaster (1966), Griliches (1971), and others to estimate the value of qualitative individual characteristics. Hedonic Travel Cost Method The direct traditional approach states that goods are objects of utility, while Lancaster hypothesized that it is the properties or characteristics of the from which utility is derived. consumption is an activity in which goods are inputs orderings are assumed to rank characteristics indirectly For only to rank a dinner party, social setting, intellectual all and and Utility or collections collection f of goods through the characteristics that they possess. example, hedonic) goods He thus could assume that the output is a collection of characterisrics. preference the a combination of meal may possess nutritional, characteristics. This approach has two fundamental and aesthetic, and characteristics (or propositions: (1) goods possess objective characteristics relevant to 105 the choices which people make among different collections of (2) individuals differ in their goods, reactions to different characteristics, rather than in their assessment of the characteristics collections. view the least a content of Using these two basic propositions, relationship between people and two-stage affair, relationship one can things it is composed i.e. goods various as at the of between things and their characteristics and the relationship between characteristics and people. This approach can be illustrated by the consumer's choice problem under a regular budget constraint Max U (52) v (Z) s.t. Z = Bq pq where the problem the objective function v(Z) of the optimizing in the characteristics approach is a function vector constraint q, M, of characteristics Z The regular pq = M is a constraint on the vector of of budget goods on which p is the vector of prices facing the consumer and M is his income Z and q are linked through the goods- characteristics relationship Z = Bq, where B is the matrix ef coefficients relating goods and characteristics The dual problem of the above will be as the following: optimizing problem 106 M = pq Mm s.t. v(Z) = U Z = Bq. A cost function therefore be can derived this from problem as: M = C (z, p) also known The derivative property of this cost function, as Shephard's approach. functions, demand price derivatives are the Hicksian Its this to is of central importance Lemma, p), while the derivative with respect to h(Z, J b C (Z, p)/ = is = b Z j (z, p) j j characteristic. the shadow (or implicit) price of jth This price measures the marginal cost of a small public goods which have been valued by using shadow increase in Z 3 Among the hedonic approach are the (Anderson 1978), and Crocker, climate (Hoch, 1971; Harrison section, with the and etc.. 1981), the hedonic approach will be cost method and applied to travel Rubinfeld, 1974), noise level (Nelson, 1979), and outdoor recreation activity (Morey, this pollution air followings: In incorporated the Oregon salmon sport fishing activity. Based upon Lancaster's version, each recreational characteristics. The site should one can assume that have a bundle added expenditures for an of enhanced 107 bundle extra the the characteristics could reveal the value of of characteristics. behind This is the driving force hedonic technique. Therefore, at recreationists a given origin, by spending more travel costs and travelling a little further, can possibly obtain a better bundle of characteristics. In other words, individuals from the same travelling different distance to origin sites will incur different travel costs reach different with different objectively measured set of characteristics, density, is water quality, thus possible, such as fish species variety and so forth. It at least in theory, the to estimate marginal cost (or implicit price) of added characteristics for recreationists from a given origin. To estimate the marginal cost of increasing a amount first characteristic of to the recreationists step of the hedonic travel cost approach. small is But the it should be noted that the estimating procedure of this step is exactly opposite with the traditional travel cost method. The traditional travel cost technique uses a sitespecific from model which approach which features one site and many recreatjonjsts come. However, the origins hedonic holds one origin constant and computes the cost origin. The derivative of the cost function with respect to each site of each of reaching characteristic all different sites from thus yields that the implicit price characteristic for that origin. 108 Therefore, each origin will yield a different set of implicit prices for site characteristics. In practice, this step is done by running a set of regressions, one for each origin, costs on characteristics, i.e., regressing travel for a given origin on characteristics of sites. Then, imputed coefficients of the regressors are the the of the characteristics for prices different that origin. This step can be expressed in mathematical terms: TC =b0 +b Z s (56) 1 ls +b Z 2 2s +...+b jZ jS denotes the travel cost from a given origin to a where TC S given site s, is the level of the jth characteristic Z is at given site b s, is the imputed price of the jth J The constant term b characteristic for the given origin 0 may represent mean the value omitted the of characteristics The each next step is to derive the marginal characteristic. quantity the Regress value of of characteristics each recreationist enjoys on ths prices of the characteristics obtained from the first step and other factors which are characteristics characteristics. estimated This determinants is the of demand demand for function for A demand function for trips can also be by regressing the number of trips on the prices of characteristics, and other factors expressed by two demand functions: This step can be 109 = f (B z , k j]c TRIPS = g (B , k Ic where R ) k R ) k is the vector of imputed prices faced by the kth B k individual, and R a vector denotes demand other of Ic determinants denotes TRIPS for the kth individual. the k number of trips for the kth individual. The compute estimated demand the value of the site. The consumer surplus each characteristic level can be obtained each characteristic demand equation, implicit price each consumer taken surplus computing by the Summing up the consumer surplus the value for the site is per trip times total for that site. for at consumer surplus of each characteristic, Then, to evaluated individual faces. per trip can be derived. used be may equations In addition, number of trips the value of changing travel costs or a characteristic at a particular site also can be estimated. Estimation of the Hedonic Travel Cost Demand Model and ocean sport fishing data are combined together to apply with site Fresh-water salmon to salmon sport fishing data travel cost method characteristics. This data set represents 158 individual .the incorporating observations from fresh-water and 211 from ocean. However, this sample of 369 was further reduced to 290 because of 110 the necessity of having a minimum number of responses from a given origin to run the which the obtained. from be can characteristics prices for implicit regression, first-stage a minimum number of 5 was arbitrarily In fact, assigned for a county (which represents the origin) to run regression. least It turned out that only 14 counties had at observations 5 traveled that sport salmon for fishing. Respondents effort their the 1977 Oregon angler in success reported rate fishing This survey. is the only variable that and success fishing site represents quality in the model (other quality variables are riot easy to appropriately define, sources). fishing Therefore, distance salmon of data 14 different implicit prices of the success rate were obtained for 14 regression first-stage site due to the limitation used the The counties. reported round trip from a given county to the given salmon fishing as the dependent variable and used reported average catch per hour for the site as the independent variable. Thus, the implicit price, measured in miles, was simply the linear regression. different coefficient of the fishing success rate in linear These regression statistically satisfactory. price 14 implicit equations prices were from not 14 all Among them, 5 of the implicit coefficients had negative signs which violated the basic assumption that the quality characteristic increases 111 linearly with substituted distance. However, negative implicit prices in for were zero values of second the stage regression. individual demand function for fishing success could then be estimated by regressing the rate of fishing The Success consumed by the individual on the implicit price, reported income, One trips and reported number of of linear demand model fitted by OLS was: = 0.1484 SE (59) 0.002314 NT - 0.00002104 IP k k k (20.18) (-2.10) n = 290 R (-2.67) 2 equation (59), = 0.036. success denotes the fishing SE k rate, denotes catch per hour, for the kth individual, NT k the and IP the kth should be noted that the income variable was number of salmon trips during that quarter, k denotes the angler. It included originally However, "in discarding is implicit price of site quality for the and a t value of 0.8 classical linear interested than the value standard theoretical of its estimate (from given data) will decrease 1971, making, model, regression the mean square error of all the least squares (Rao, obtained. an independent variable whose parameter smaller (in magnitude) than the deviation was he p 38) Besides, "when a estimates" researcher in using the regression estimates in wants the mean square error estimates best linear unbiased estimates" (Ibid, is decision rather p.39). 112 Therefore, the income variable was deleted from the model. This demand for fishing success can be converted to demand for catch per trip by using a sample average of 6.8 hours per which is measured in miles, (59). If this consumer surplus is evaluated at $0.1 mile, then upon trip. the traditional and $197 per based method, of Applying the sample mean catch per trip to the values per trip, about from $103, estimate Gum-Martin and trip, computed thus can be the values per trip are $77 and respectively. 0.39 The average consumer surplus per $264 average values per fish are Gum-Martin and traditional for estimates. The corresponding demand function for trips was estimated as follows, NT (60) = SE -0.004949 5.5094- 4.8713 k PSAL Ic Ic (9.54) (-2.21) (-1.56) - 0.03433 PCON Ic (-2.73) where PSAL n = 290 is the marginal price of success in terms of Ic money for lcth person, denotes the marginal price of PCON Ic other quality variables in terms of money (the constant term in each of the first-stage regression represents mean value of the omitted characteristics). in (60) are defined the same as for the Other symbols equation (59). It seems reasonable that trips should vary inversely with the price of success and other variables, but it is not at all 113 why clear rate trips should fall as the fishing success increases. and (60) are two simultaneous demand equations (59) derived from the same utility function, and they represent the angler's these fishing choice of salmon two simultaneous equations were fitted Simultaneous Since activity. equation bias was suspected by OLS, (Koutsoyiannis, 1977). Thus, other estimation methods should be applied to obtain unbjasdd and consistent linear models estimates. by estimated (59) and (60) were of Therefore,the the method of two-stage least squares (2SLS) and yielded, = 0.2115 - 0.01845 NT - 0.00003172 IP SE k Ic (6.72) NT 5.1991 = n = 290. (-2.74) (-2.36) - 2.2417 Ic SE - 0.004758 (1.42) (-0.73) PSAL Ic Ic (-1.51) - O.03627PC0N Ic n = 290. (-1.41) Equation surplus. (61) Based can be used to measure the upon the Gum-Martin method, the consumer average consumer surplus per trip is $68, and $175 per fish. These results indicate that the estimated net economic benefits from the OLS equation may be overstated, at least compared to 2SLS. In summary, the application of the hedonic approach to Oregon salmon sport fishing was not very successful, at least for this study. There are several possible reasons 114 that application. may explain the gap between theory and First, 1977 the survey data collected from the used here was which was primarily Oregon angler survey, designed method for the application of the traditional travel cost rather than for characteristics. the hedonic method site incorporating Thus, for example, the quality variables the based upon for the various site were hard to define, available data. Second, travel some method cost example, it linearly with is not because from some the unit the externalities (e.g. cost of a But this is not a reasonable richer individuals may enjoy nearer Besides, sites. of a characteristic can be cost For increase characteristics that so hedonic the logical. completely that is constant. characteristics constant assumed distance characteristic assumption, are of assumptions basic true congestion at the site, only the if and traffic jams on the road) do not exist. Third, the data for ocean fishing and fresh-water fishing were combined together for the hedonic travel cost demand but these two types of sport model, fishing are probably not homogeneous goods. Last, was noted it in chapter 4 likely for an indirect method, cost the method, process that it is such as the hedonic travel to incur serious measurement errors of very data gathering. In fact, the during fishing 115 success rate, may have data fishing success divided by fishing Using been underestimated by the anglers. from the Oregon Department of Fish effort, and the Wildlife, average catch per trip would be about 0.7, which is almost twice as much as the sample mean catch per trip. This fact shows that data, or both, study of testing three major data about marine (1977) be the fishing success data, effort or fishing may have serious measurement errors. In a recreational approaches collection fishing, Hiett and Worrall found that total effort and total catch should not taken from considerable a household tendency survey because of the is very toward bias. This bias likely from the recall errors. Thus, "such estimates (of effort and catch) should be obtained from study ...' (Ibid, p.22). the intercept 116 SUMMARY AND CONCLUSIONS VI. The analysis upon this study has focused of estimates of demand for and economic benefits from salmon sport Oregon consumer of estimates Various fishing. the surplus per trip and per fish were obtained from different estimation methods. analysis time The is based upon the the travel cost method cost salmon the traditional single site type of from method presented in Table are fishing approach zonal 7 average The values from the adjusted individual from the from the approach are even higher than for approach, individual travel fresh-water for over twice as high as the values are unadjusted estimated The and money costs of travel to a site. results demand for technique primary while the values the adjusted individual observations The high individual resulted is surplus from the to have travel cost estimates observations in Table 7 are believed in measurement are consumer part from the bias caused error by Since most of the measurement averaged out in the zone average method, believed to be more reliable than the errors this method individual observation approach In addition to the bias from measurement is thought estimated error, that another reason for the consumer from the unadjusted individual it surplus observations 117 Table 7. A Comparison of Consumer Surplus Values for Fresh-water Salmon Sport Fishing, Estimated by Various Models Using Reported Travel Costs Traditional Consumer Surplus Gum-martin Consumer Surplus average per trip average per trip Model Zonal Average 21 21 Adjusted Individual 47 48 Unadjusted Individual 61 91 Table 8. $ A Comparison of Consumer Surplus Values for Ocean by Salmon Sport Fishing, Estimated Various Models Using Reported Travel Costs Model Average Traditional Consumer Surplus Per Trip Zonal Average Adjusted Individual Unadjusted Individual $ 62 Average Gum-Martin Consumer Surplus Per Trip $ 57 78 85 217 293 118 being so high is because this procerdure does not properly account As explained in some from the more distant zones. in come the lower percentage of the people who for chapter individual 4, detail by observations generated linear demand function and a specified random distribution of demand estimation approach, percent intensity resulted in a 42 percent error of by the unadjusted individual observation (Ulo) while the error of estimation was only about These method. with the traditional zone average 1 results illustrate that estimates of consumer surplus from the UlO approach can be seriously overestimated when there is participation a significant decline in the percentage rates of the more distant zoneS. A summary approach, (ulo participation basis) all UlO approach rates included, estimation of probability with average zone traditional and individual observations adjuted to per capita method, Table of four different methods of applied 9. but in The estimates of consumer surplus obtained from the UlO approach were very close to each UlO approach gave an estimate while the times that of any one of the other three, Gum-Martin measure emphasized that measured presented to ocean salmon fishing is of consumer these surplus. results were of other, four about based upon the It obtained should by be using distance instead of reported travel costs in the travel cost demand models. The advantage of using measured 119 Table 9. A Comparison of Consumer Surplus Values for Ocean Salmon Sport Fishing, Estimated by Various Models Using Measured Distance Model Average Traditional Consumer Surplus Per Trip Zonal Average Ad3usted Individual Unadjusted Individual UlO with Probability of Participation Rates $ 57 Average Gum-Martin Consumer Surplus Per Trip $ 52 49 53 152 208 54 54 120 distance that is reported travel comparison the bias from costs can be measurement errors avoided that so in the among the various results is concentrated only upon other causes for the difference, such as the decrease in participation rates as distance increases. The comparison of various estimates consumer of surplus, discussed in chapter 4 and summarized in Table 9 has several implications. First of all, the estimate of consumer surplus based solely upon the UlO approach cannot be considered observations reliable. using Second, individual the by themselves can lead to incorrect consumer surplus estimates unless they are adjusted to a per capita basis, just Third, if the UlO approach is used, of participation approach (The of rates should then the probability linked be to order to estimate a valid consumer in reasoning and procedure for linking the participation unadjusted as a function individual model. cost as for the zone average travel of observations distance was the UlO surplus. probability with the presented in chapter 4, and the results are partially summarized in the last line of Table 9.) However, if there is an percentage of participation from all distance zones, the individual observations can be used alone and equal then would not need to be adjusted. The problem of measurement error in travel costs was discussed and analyzed empirically, and measured distance 121 to used as an instrumental variable for travel costs was solve the measurement error problem. The results for ocean salmon fishing showed that the Gum-Martin individual surplus estimated from the adjusted per capita observations zone was average the from about 50 percent higher than approach, consumer were when reported travel costs as shown in Table 8. However, the difference in the used, Gum-Martin consumer surplus between these two methods was 2 percent when the instrumental variable was about only of This result implies that most as shown in Table 9. used, per adjusted the difference in results between the capita individual observations and the zonal average model was due to the bias from measurement errors in the travel cost variable. surplus Moreover, between these the two difference in essentially was methods consumer eliminated by using the instrumental variable approach. The benefits tested relationship and between fresh-water net estimated salmon catch was as a linearly homogeneous equation in Marginal values per fish, economic empirically chapter 3. equal to the average values per could thus be obtained. It should be noted that the fish, values per fish were made by a two stage procedure. In the first stage, the consumer surplus per river was computed from traditional travel cost demand model. stage, consumer surplus salmon catch per river. per river was In the regressed second upon The fish catch was not a variable 122 in the demand equation of the first stage. value marginal The of a fish was simply computed from the increase comsumer surplus associated with the the in increase in number of fish caught. Thus, the number of fish caught was not to the demand function in the related Therefore, values this derived value from the from may be quite different demand functions in stage. first fishing which success was included as a variable. per reliable estimates of the marginal value based upon the traditional zone average model most The fish, and the two stage estimating procedure noted above, ranged between $90 and $100 per fresh-water salmon. However, the values per fish estimated from the individual observations were again much higher than those estimated from the zone averages, but are not thought to be accurate for already outlined. that The homogeneous equation reasons of degree one was used implies that if the catch is doubled, the consumer surplus would also be doubled. then This approach implies that as long as the salmon catch can be predicted, the consumer surplus can be estimated from homogeneous equation. In addition, the linearly if it is decided to increase anglers' benefits, then those factors that affect the salmon catch should be improved. If the variable of catch per river times distance from Portland, measured in miles, was also included in the above linearly homogeneous model, then each additional 123 from the Portland Metropolitan area was estimated to mile reduce the value per fish by about 32 cents. This estimate of the distance from Portland effect, high because southern fished of anglers from California that Oregon rivers but who were not included analysis. fishing however, may be too in the in In other words, the consumer surplus for salmon on been have may southern Oregon streams the relatively underestimated. From one analysis of value per fish in chapter the value can conclude that most of the variation in the per fish by river was due to sampling errors, 3, both in the consumer surplus by river and in the catch estimates based upon salmon and steelhead tag returns. data were available for all the nine rivers, If survey creel then both the consumer surplus and the salmon catch estimates could be corrected give more accurate values per to fish. In chapter 5, quality and substitute site variables, were directly into a regional incorporated model. derived regional Marginal from value this type per of travel cost method, fish thus demand can cost travel be equation. directly For the average value per the trip was around $24. The marginal value per salmon caught for a certain river can be estimated from the regional travel cost model as follows: 1) hypothetically increase the fish catch in that river, 2) keep the other rivers' fish catch unchanged, 3) use the regional travel cost demand equation 124 and new level of fish catch in that river to compute new consumer surplus, is 4) the incremental consumer surplus divided by the incremental then the increase salmon in catch in that river. The regional estimates fishing travel cost method results show marginal about value However, percent of the underestimate specification, important to of or average being only marginal value poor data, This value. be may or both. cost travel presented in chapter 5 seemed too low, 25 computed the fish from the regional per data as long as catch and distance the new sites are available. models future or sites can be obtained from present models without need for new surveys, for new net economic benefits from of that due possible poor to it However, is from note that the average values per fish the regional travel cost models were surprisingly close to the average values from the earlier traditional single site type of models that were fitted to the same data presented can in chapter 3, even though these earlier models be criticized from a specification point of view not including substitute and quality variables. further other research with activities is needed, was that total little data for with for Although recreational one important finding of this study the traditional travel cost model estimates and and average consumer surpluses were the addition of the substitute changed and of very quality 125 variables in the more completely specified regional travel cost models. travel cost This finding indicates that the traditional model may be rather robust total and average consumer surplus. estimated (The stability of the cost coefficient and the travel estimating for corresponding consumer surplus estimate is illustrated in Appendix F.) A hedonic Hedonic travel cost model cost travel models was usually characteristics as quality variables. estimated. also site include However, only the quality variable that was used in this study was a fishing success catch computed by dividing the salmon variable, reported by the angler by his reported hours of fishing on that trip. Based upon this hedonic travel cost model which was first estimated by OLS in this study, the average GumMartin consumer which fish, value. seems However, success least surplus was $103 per trip and to be an unusually high when per $264 estimate of fishing the demand functions for and for fishing trips were estimated by two stage squres simultaneous (2SLS), equations, i.e., they were considered the average Gum-Martin as consumer surplus was reduced to $68 per trip and $175 per fish. One thing that needs to be noted is that the value per fish in the hedonic travel cost method is derived from the demand for the fish catch rate (reported salmon divided the by reported hours of salmon fishing) rather demand for fishing trips. Therefore, the catch than marginal 126 value per catch rate. But for the traditional single site type of the marginal value per fish cannot be travel cost model, Despite this obtained by simply increasing fishing trips. advantage, fish the fish can be estimated by increasing be to hedonic travel cost method seemed the much more sensitive to problems with specification and the Therefore, data. estimates travel it needs to be noted that the numerical value of model cost of trips and fish from and were rather unstable hedonic the be should considered to be rather questionable for this study Despite problem of estimation, regional and directly related these the hedonic travel the valuation by the methods cost catch, (because to recreation site management such demand functions involve variables, be can as fish over which management may have some control). This feature is especially important for resource managers. As noted earlier, one cause of the problems with the hedonic very approach was that this approach is thought to demanding of good data. pertaining data It needs not only the needs travel not characteristics Also, sites. it trips and but objective data that would quantify the Therefore, the only data pertaining to number cost, data but also the to anglers from various origins, concerning their trips to various be of the various sites. of expense of gathering an appropriate set of data hedonic travel cost model could be quite large. for the On the 127 other hand, fitted to a rather rough set of data, be empirical and the of this study indicate that this model was rather results robust can model traditional travel cost the relable for estmat1ng and consumer total the surplus and average consumer surplus per trip or per fish. Considering predictive the analytical the power, usefulness, and the need for data, the traditional travel cost may be more reliable than the hedonic model travel cost model for most studies of recreational fishing. The regional and hedonic travel cost methods with quality variable approaches for were studying shown to be the to make future research more improvements behavior, recreationists' although the success in this study was quite order promising possibly limited. successful, in methodology along with In further appropriate data are required. For price example, approach may the utility function for the be simultaneously traditional and Lancaster's consumer commodities factors travel hedonic constructed theory, i.e., of the utility function. cost method, quality Therefore, method both and characteristics can be joined together as Also, in the hedonic it is important that sufficient data should be avalable for the various origins and sites, the from data characteristics must be and quantifiable. suitable for the traditional travel cost are often not appropriate for application of the 128 hedonic first travel stage function is cost method. The reason is that of the hedonic travel cost method, constructed for an origin so that in the a cost the data must cluster around the origin. But the traditional travel cost method is based upon site-specific area studies, the data the are always acquired from different otigins specific site. quantify some In addition, the of site to it seems very difficult to such as characteristics, scenery, and congestion. However, dummy variables might be used to approximate some of these quality variables. In travel short, cost the more complex regional models seem to require a better and hedonic quality data to accurately estimate the value of quality of changes Therefore, the approach to collect data should be designed appropriately, and must be minimized the recall errors of the respondents 129 BIBLIOGRAPHY Anderson, R., and T. "Air Pollution and Crocker, Studies, Residential Property Values", Urban 8(1971):171-180. Becker, G. S., "A Theory of the Allocation of Economic Journal, 75(1965) :493-517. Time", Bishop, R. 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"Estimating the Value of Variations in Anglers' Success Rates: An Application of the Multiple-Site Travel Cost Method", Marine Resource Economics, 2(1985) :55-74. (forthcoming) Samples, K., and R. Bishop, Sargan, 3. D., "The Estimation of Economic Using Instrumental Variables", 26(1958):393-415. Relationships Econometrica, Sinden, 3. A., "A Utility Approach to the Valuation of Recreational and Aesthetic Experiences", American Journal of Agricultural Economics, 56(1974):61-72. Sorhus, C. N., Estimated Expenditures by Sport Anglers and Net Economic Values of Salmon and Steelhead for Specified Fisheries in the Pacific Northwest, Ph.D. Thesis, Oregon State University, Kerr Library, Corvallis, 1981. 134 Brown and K. C. Gibbs, Estimated C. N., W. G. Expenditures Oregon Northwest, in the Pacific Agricultural Experiment Station Special Report 631, Covallis, July 1981. Sorhus, Stevens, J. B., "Recreation Benefits from Water Pollution Control", Water Resources Research, 2(1966):167-182. U. Burean of Outdoor Recreation, Apendidx"A" - An Economic Analysis, in Outdoor Recreation: A Legacy for America, Washington, D.C., 1973. S. Vickerman, R. W., "A Demand Model for Leisure Travel", Enviroment and Planning A, 6(1974):65-77. Willig, R. D., "Consumer's Surplus Without American Economic Review, 66(1976):589-597. Apolgy", Working, E. J., "What Do Statistical Demand Curves Show?", Quarterly Journal of Economics, 41(1927):212-235. in Variables Zarembka, P., of "Transformation Econometrics", ed. by in Frontiers in Econometrics, P. Zarembka, New York: Academic press, 1974, pp.81 104. APPENDI CES 135 are 38 zonal average observations for There fresh- water salmon analysis in Oregon shown in APPENDIX A. These zonal 38 data were 158 from constructed individual observations and were used to estimate the regional travel However, the 158 individual observations from cost model. fresh-water salmon anglers were originally divided into 37 with most of zones having four or five zones respondents who had actually fished during the period of survey. Those 37 zonal data were mainly used to estimate the traditional zone average became (Xl); into two zones. average 37 zones then average The variables in APPENDIX A travel cost from ith zone replacement related equipment (x2); ith Those 38 zones as shown in APPENDIX A after one zone was partitioned denote travel cost demand. to value of salmon jth fishing river and average reported family income of zone fishing in jth river (X3); average measured one way distance from ith zone to jth river (X4); total salmon catch in jth river in 1977 (X5); average measured one way distance from ith zone to kth substitute river (X6); total salmon catch in kth substitute river in 1977 (x7); average trips per population capita for from ith to zone ith zone to jth river variable for ith zone to jth river (xlO), 1, jth (X9); river (X8); and dummy which equals to if X9 > 95,000, and 0, otherwise. APPENDIX fresh-water B includes 158 individual observations for salmon sport fishing in Oregon . Those 158 136 individual data adjusted were used to estimate the and unadjusted individual observation travel cost model. There are variables included in six APPENDIX B, Xl denotes number of salmon fishing trips for ith individual to river; X2 denotes reported travel cost for ith individual to and fishing salmon X3 represents replacement value of jth river; jth related equipment for ith individual to jth river; X4 represents family income for ith invidual to jth river; X5 is the share of distance zone population for ith individual X6 is the trips per capita to jth river; for ith individual to jth river. APPENDIX observations has C ocean 47 which were used for zone average travel cost Those 47 zonal data models in chapter 3 and in chapter 4. were constructed from 211 variables observations. individual The in APPENDIX C can be expressed as population of ith distance zone to jth port (Xl); way average zonal salmon distance from ith zone to jth average measured twO port (X2); average number of trips per capita from ith zone to jth port (X3); average (X4); reported travel costs from ith zone average opportunity to jth cost of travel time from port ith zone to jth port (X5). APPENDIX observations Those 211 unadjusted D for is composed of 211 ocean salmon sport fishing individual data were used for individual in Oregon. adjusted individual observation travel cost methods and in 137 chapter can 3 and in chapter 4. The variables in APPENDIX be denoted as followings: number of D fishing salmon trips for ith individual to jth port (Xl); reported travel costs for value of ith individual to jth port salmon fishing and related individual to individual to jth port (X4); jth port (X3); replacement (X2); equipment family income for ith for ith the share of distance zone number of population for ith individual to jth port (X5); anglers who went together on that trip for ith individual to port jth individual (X6); measured two way jth port (X7); to blow-up distance for ith factors for ith individual to jth port (X8). APPENDIX fished Those E contains 290 individual observations who for salmon in Oregon during the period of survey. 290 individual data were used for the second regression variables the in in hedonic APPENDIX individual (Xl), travel cost E are success per stage The method. hour kth for based upon the reported success from the questionnaire; average success per hour for kth individual (X2), family based upon all reported successes at income for kth individual (X3); fishing trips for kth individual (X4); kth individual (X5), by automobile travel number of site; salmon rate of travel for which is 40 miles per hour if travel or pickup, by camper; the and is 35 miles per hour if cost per mile for kth individual (X6), which is $0.0975 if auto or pickup was used, and is $0.116 138 if camper was used; hour miles; implicit price of salmon for kth individual in jth county (x7), mean catch measured per in value of the omitted characteristics for kth individual in jth county (X8), measured in miles. 6E1 XIaW3ddV V IX ?X EL 6? 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L00 ?LOO 00001 0 tr6VO 0051? 0 0 0 I Oft 1 5L60O 5L600 SL600 St600 9L600 5L600 91L0 5L600 SL6OO 5kB 5kB 5kB 5kB 9kB SIT9 OS Os OS OS OS OS OS OS OS OS 5L600 5L600 9ft9 Sft8 9tr9 SJ.600 51r9 5L600 5L600 SL600 5L600 5kB 9kB 9kB 09 91y9 OS OS OS OS OS 156 APPENDIX F = -1.1900 - 0.05044 RTC ln(TRPSCAP) (F-i) ii ii (-9.56) (-4.89) + 0.0002406 SSFE - 0.00002058 INC (-1.41) (2.83) -1.07184 X - 0.8876 X 1 -1.7594 X 3 2 (-6.23) (-3.65) (-3.72) 2 n R 37 (F-i) included one more variable, Equation family income (INC), page 36. However, should average and can be compared to equation (1), the t value of the income variable was significant at the 10 percent probability not of = 0.826. level. It be noted that the difference in the absolute value travel the cost coefficient in equation (1) and equation (F-i) is only about 0.4 percent. The stability of the travel other observed variables in the single site travel cost model when are When all the other variables, except the revised deleted. travel coefficient can also be cost by one, the of the travel cost coefficient along with the cost estimates variable, are deleted one corresponding estimates of the Gum-Martin consumer surplus and the coefficient of determination for each equation are shown in Table F-i. Even from 0.816 though the coefficient of determination to 0.446 in Table F-i as the variables drops are 157 deleted, estimated the travel cost coefficients consumer surplus remain relatively corresponding and stable. This stability indicates that the simple travel cost model may be rather robust for estimating total consumer surplus. Table F-i. Some Regression Results and the Estiamtes of Oregon Consumer Surplus for Gum-Martin Fresh-Water Salmon Angling in 1977 2 Gum-Martin Consumer Surplus Variables Deleted from (F-i) Estimated Travel Cost Coefficient None -0.05044 (_9.56)* 0.826 $ 4,704,500 INC -0.05024 (_9.38)* 0.816 4,723,200 INC, SSFE -0.04986 (_8.6l)* 0.778 4, 759, 200 INC, SSFE, X3 -0.04751 (_7.32)* 0.707 4,994,600 INC, SSFE, X2, X3 -0.04900 (_6.59)* 0.603 4,842, 700 INC, SSFE, Xi, X2, X3 -0.04562 (_5.31)* 0.446 5, 201, 500 * R Values of t are given in parentheses estimated travel cost coefficients. below the