S Duffield, John 338.437 A contlntient 9927 valuation F2cva assessment of 1990 Montana deer hunt In J CONTINGENT ASSESS STATE CCCU?^lMTS COLLECT! HELENA. MONTANA 59520 VALUATION NT OCTOBER 1990 cMoritaqa*DepartnieJit of : MONTANA STATE LIBRARY ■ fJUN'2 5 1997^ llliilllllillllillitiiililtiili ' 3 0864 00072641 7 APR 1 : ]999 MONTANA BIOECONOMICS STUDY A CONTINGENT VALUATION ASSESSMENT OF MONTANA DEER HUNTING; HUNTER ATTITUDES AND ECONOMIC BENEFITS Prepared for Montana Department of Fish, Wildlife and Parks By John Duffield Department of Economics University of Montana and Chris Neher Bioeconomics Associates Missoula, Montana October, 1990 EXECUTIVE SUMMARY Purpose of the Study The main objective of this study was to estimate the net economic value for deer hunting in Montana. Net economic value is the amount of money a person would be willing to pay over and above what they actually must pay in order to purchase or experience something. In this study that "something" is defined as a deer hunting trip. In addition to estimating the value of the most recent trip taken by hunters, this study also estimated the net economic value of several hypothetical deer hunting trips. This valuation of hypothetical trips was accomplished by asking hunters how much more money they would be willing to pay if (for example) their chances of bagging a large buck were to double. In all, one value for actual trips taken and 3 values for hypothetically improved trips were estimated in this study. Data Sources The questionnaire used in this study was administered by the Montana Department of Fish Wildlife and Parks after the end of the 1988 general hunting season. The population targeted by the questionnaire was those people who had purchased a 1988 deer hunting tag or big-game combination license. Hunters first received the questionnaire booklet (see Appendix A) and cover letter along with a stamped, addressed return envelope. One week later a postcard reminder was sent to those hunters not yet responding. Finally, a second copy of the questionnaire was sent to nonrespondents. An initial sample of 5000 questionnaires was mailed to hunters. Residents received 4325 (86.5%) of the surveys and nonresidents 675 (13.5%). This division closely mirrors the actual percentages of resident and nonresident hunters. Of the 5000 mailed questionnaires 44 were undeliverable and 3328 were completed and returned for a response rate of 66.5%. Descriptive Statistics Hunters were broken down two separate ways for the analysis of the data; the total sample was divided into residents and nonresidents and the total sample was divided into hunters who hired guides and those who did not. Comparisons of the characteristics of these four groups showed significant differences. Not surprisingly, nonresidents spent significantly more for their hunting trips than did residents. Nonresidents spent an average of $1006 per trip or $146 per day while residents spent and average of $112 per trip or $25 per day. There were also significant differences between the four groups in their average incomes. A complete discussion of the comparison between hunter group characteristics is contained in Chapter 4 . Hunting Trip Valuation Hunters responding to the DFWP Deer Hunting Survey were asked to value four different deer hunting scenarios. The first, was simply the value of their most current deer hunting trip. In order to determine this value, hunters were asked the following question. Suppose that everything about this last hunt was the same except your share of the expenses had been $ X more, would you still have made this trip? In this question "X" was a value between $5 and $2000. The answers to this question were analyzed to determine the average value, or net economic value, of the hunters most current deer hunting trip. The state average net economic value for deer hunting is $302 per trip. This can be interpreted to mean that the average hunter would be willing to spend $302 more than they have already spent for their most recent deer hunting trip. The net economic value of deer hunting trips varied widely between the four hunter groups. Residents were willing to spend $209 per trip more, nonresidents $706, guided hunters $800 and nonguided hunters $269. Questions similar to the current trip question above were asked in order to value the hypothetical hunting trips. These hypothetical trips included doubling the chances for a large buck, providing a very good chance of bagging a small buck or doe and allowing the taking of an extra deer. Responses to the improved conditions questions showed some clear trends. Respondents in all categories consistently valued doubling their chance for a large buck above the chance for an extra deer. Both of these alternative scenarios were valued significantly higher than a good chance for a doe or a small buck. The magnitude of most of the improved conditions values, however, were lower than current trip values. This makes comparisons between the improved conditions questions and the current trip questions difficult. Analysis of Different Types of Hunters In addition to the preceding analysis, hunters were "clustered" according to their motivations for hunting and then analyzed as different hunter types. Four basic "types" of deer hunters were identified: specialist meat hunters, specialist trophy hunters, general hunting enthusiasts and generalist meat hunters. A detailed description of these different hunter groups can be found in Chapter 7. The different hunter groups showed significantly different net economic values for their most recent deer hunting trip. Values were $298 for the general hunting enthusiast, $182 for specialist meat hunters, $471 for trophy hunters and $315 for the generalist meat hunters. ACKNOWLEDGEMENTS The authors would like to thank Rob Brooks for his excellent data management effort. We would also like to acknowledge the helpful comments obtained from Montana DFWP biologists, including Ken Hamlin, and Dave Pac. TABLE OF CONTENTS Page EXECUTIVE SUMMARY i ACKNOWLEDGEMENTS iv TABLE OF CONTENTS V LIST OF TABLES vii CHAPTER I : INTRODUCTION 1 Objectives 1 Definition of Economic Benefits 1 CHAPTER II: MEASUREMENT OF NET WILLINGNESS TO PAY: THEORY AND METHODS 3 The Contingent Valuation Method 3 Estimation of Willingness to Pay Using Dichotomous Choice CVM 4 CHAPTER III : DATA SOURCES 5 Questionnaire Administration 5 Response Rates 5 CHAPTER IV: DESCRIPTIVE STATISTICS 6 Hunter Characteristics 6 Trip Characteristics 9 Hunter Expenditure Data 11 Hunter Management Preferences 12 CHAPTER V: MONTANA DEER HUNTING VALUATION ANALYSIS: MODEL SPECIFICATION AND ESTIMATION 14 Contingent Valuation Questions Asked 14 Outlier and Protest Responses 15 Specification of the Model 16 Estimated Equations 18 Benefit Estimates 23 Analysis of Values Across CVM Questions 25 Analysis of Values Across Regions 28 Analysis of Dispersion Around Nonparametric Means .... 29 Comparison of Results to Previous Studies 37 CHAPTER VI: MARKET SEGMENTATION: CLUSTER ANALYSIS OF HUNTER TYPES 40 Market Segmentation 40 Cluster Analysis Design 40 Description of Hunter Types 43 Economic Analysis of Cluster Groupings 43 CHAPTER VII : CONCLUSIONS 50 REFERENCES 51 APPENDIX A: SURVEY INSTRUMENT 54 APPENDIX B: ESTIMATED BIVARIATE MODELS 61 LIST OF TABLES Table Title Page 1 Montana Deer Hunting, Crosstabulation of Residency and Guide Classifications 7 2 Montana Deer Hunting, Hunter Characteristics 8 3 Montana Deer Hunters, Percentage that Killed Other Game , by Species 8 4 Montana Deer Hunting, Trip Characteristics 9 5 Montana Deer Hunting, Montana DFWP Administrative Region Characteristics 10 6 Montana Deer Hunting, Trip Expenditures by Hunter Subgroup 11 7 Montana Deer Hunting, Management Preferences by Hunter Subgroup 13 8 Montana Deer Hunting, Current Trip Estimation by Hunter Group 19 9 Montana Deer Hunting, Double Chance of Buck Estimation by Hunter Group 2 0 10 Montana Deer Hunting, Good Chance of Doe Estimation by Hunter Group 21 11 Montana Deer Hunting, Chance of Extra Deer Estimation by Hunter Group 22 12 Montana Deer Study, State Average Net Economic Values Per Trip and Per Hunter Day: Current Trip Question 24 13 Montana Deer Hunting, Net Economic Values Per Trip: Improved Condition Scenarios 26 14 Montana Deer Study, Montana Deer Hunting Values by Region 3 0 15 Montana Deer Hunting, Nonparametric Means and Confidence Intervals 33 16 Montana Deer Hunting, Nonparametric Means and Confidence Intervals 35 17 Montana Deer Hunting, Comparison of Results with Previous Big Game Studies 39 18 Montana Deer Hunting, Comparison of Hunter Characteristics Across Clusters 42 19 Montana Deer Hunting, Current Trip Estimation by Cluster 4 5 20 Montana Deer Hunting, Double Chance of Buck Estimation by Cluster 46 21 Montana Deer Hunting, Good Chance of Doe Estimation by Cluster 47 22 Montana Deer Hunting, Chance of Extra Deer Estimation by Cluster 48 23 Montana Deer Hunting, Net Economic Trip Values By Cluster 49 B-1 Montana Deer Hunting, Estimated Bivariate Models Current Trip Question 62 B-2 Montana Deer Hunting, Estimated Bivariate Models Double Chance of Buck Question 62 B-3 Montana Deer Hunting, Estimated Bivariate Models Good Chance of Doe 63 B-4 Montana Deer Hunting, Estimated Bivariate Models Chance of Extra Deer 63 B-5 Montana Deer Hunting, Estimated Bivariate Models By DFWP Region 64 B-6 Montana Deer Hunting, Estimated Bivariate Models By Hunter Clusters 65 Vlll CHAPTER I INTRODUCTION Objectives This report presents a broad picture of both the qualitative and quantitative aspects of deer hunting in Montana. People who hunt deer in Montana are a very heterogeneous group. Some travel 3000 miles to hunt and others walk out their back door. Some spend $ 10 on a trip and others $ 2000. Some hunt for meat, some for trophies and others for less tangible reasons. This study presents trip characteristics, hunter characteristics, and expenditure data for several subgroups of hunters. The presentation of these descriptive statistics and trip values gains interpretive value when hunters are grouped by such factors as residency, trip type, and motivation for hunting. The qualitative dimension of this study assessed the values which deer hunters place on their current hunting trips as well as the value which they would place on trips which in some way had improved hunting opportunities. These specific improvements were doubling the chance of bagging a large buck, improving the chances of bagging a doe or small buck and allowing a second deer to be taken. Net economic values for hunters most current trip as well as for the three improved trip scenarios are presented for the entire sample, resident/nonresident and guided/nonguided subgroups and for the seven Montana DFWP administrative regions. This study provides three primary contributions to existing data on Montana deer hunting (Brooks, 1988) : (1) Descriptive statistics are reported for hunter characteristics, trip characteristics and hunter management preferences. (2) Changes in net economic values associated with improvements to the deer hunting experience are reported . (3) Economic values are stratified by different types or "clusters" of hunters. These clusters define hunters with similar motivations, expectations and preferences. Definition of Economic Benefits The U.S. Water Resources Council Principles and Guidelines (1983) require many Federal agencies to employ net willingness to pay in measuring the value of both marketed and nonmarketed (e.g.. recreation) resources. When performing natural resource damage assessments the U.S. Department of Interior mandates the use of net willingness to pay in calculation of societal gains and losses (U.S. Department of Interior, 1986). Additionally, the Bureau of Land Management (1982) also uses net willingness to pay in measuring the economic benefits of wildlife when performing cost benefit analysis. Use of net willingness to pay in cost benefit determinations is also recommended in current economic literature (Just, Hueth and Schmitz, 1982; Sassone and Schaffer, 1978) . Many recreationists, when asked if a specific recreational experience was worth more to them than they actually had to spend answer "yes". Net willingness to pay is a measure of that additional amount, over and above what they actually had to pay, which they believed the experience was worth. Therefore, net economic value or "consumer surplus" is the difference between what a person is willing to pay and what they actually must pay. This net willingness to pay is the measure of benefits associated with deer hunting which is used in this study. CHAPTER II MEASUREMENT OF NET WILLINGNESS TO PAY: THEORY AND METHODS The two most widely used methods for estimating net willingness to pay for outdoor recreation are contingent valuation (CVM) and the travel cost model (TCM) . These are also the two general methods recommended by the U.S. Water Resources Council (1983) for valuing recreation in federal cost benefit analysis. While the Montana Deer Hunting Survey gathered the information necessary to make both CVM and TCM estimates of net willingness to pay only the CVM analysis was undertaken in this study. Brooks (1988) used travel cost methodology to estimate net willingness to pay for Montana deer hunting and the CVM application of this study complements Brooks' work. The Contingent Valuation Method In the CVM approach individuals are directly surveyed on their willingness to pay for the services of a given resource contingent on the existence of a hypothetical market situation. This flexible technique has been applied to a wide range of environmental and resource issues including air and water quality changes, scenic beauty, and wildlife (Cummings, Brookshire and Schultze, 1986) . The only limitation of the method is the ability of the researcher to frame understandable questions and the ability and willingness of the respondents to accurately value the good or service. Bishop and Heberlein (1985) have described six key methodological choices in a CVM application: 1) target population, 2) product definition, 3) payment vehicle, 4) question format, 5) method of analysis and 6) supplemental data. The target population for this study is the direct users of deer hunting resources (Montana deer hunting license holders) while the product definition is a deer hunting trip. It is generally agreed upon that the payment vehicle must be specified for the respondent. Mitchell and Carson (1981) suggest two criteria for an appropriate vehicle: realism and neutrality. For this study increases in deer hunting trip costs were used as the payment vehicle. This vehicle presented respondents with a realistic and emotionally neutral (as opposed to increases in taxes) payment method. The question format used in the CVM in large part also determines the method of analysis to be used. The question format can be one of three basic types. First, the open-ended CVM is the simplest approach: respondents are asked their maximum willingness to pay for the use of a given resource. This approach can be administered at a low cost and is relatively easy to interpret. A widely used alternative to the open-ended format is the iterative bidding game where interviewers ask respondents for a yes or no response to a specified bid amount. If the respondent is willing to pay that amount the bid is raised in increments until the persons maximum willingness to pay is reached. Iterative bidding is a costly question format which requires face to face or telephone contact between interviewers and respondents . A third question format, the dichotomous choice approach, combines some of the better features of both open-ended and iterative bidding. In dichotomous choice, the individual is faced with a single specific dollar bid and (like bidding games) the response is a simple market-like yes or no. The dollar bid amount is systematically varied across respondents. This format is amenable to mail surveys and is therefore relatively low cost. This relatively new approach has been successfully applied to valuation of hunting permits (Bishop and Heberlein, 1980) , boating and scenic beauty (Boyle and Bishop, 1984) , and beach recreation (Bishop and Boyle, 1985) . In this study the dichotomous choice approach was used to value deer hunting trips. Although there are advantages and disadvantages to each method recent research shows dichotomous choice models can provide fair approximations to actual market transactions (Bishop and Heberlein, 1980; Welsh, 1986) . In general, comparisons of real markets to simulated CVM markets indicate that respondents attempt to give their true value of resources being studied. A discussion of the specific CVM questions asked and the application of CVM analysis to Montana deer hunting is presented in chapter 5. Estimation of Willingness to Pay Using Dichotomous Choice CVM The major disadvantage of the dichotomous choice method is that analysis is more complex than with open-ended or iterative bidding methods. In view of the considerable advancements in methods for modeling discrete choice (Amemiya, 1981) this complexity is manageable and acceptable when compared with the advantages which dichotomous choice CVM questions afford. These advantages include: a realistic market-like scenario and a high percentage of responses to the CVM questions. Dichotomous choice methodology estimates expected maximum willingness to pay in two steps. In the first step, a logistic regression is run between the probability of a yes would pay $X response as the dependent variable and the amount $X as the independent or explanatory variable. Once this logit curve is estimated the area under that curve is the expected maximum willingness to pay. CHAPTER III DATA SOURCES Questionnaire Administration The questionnaire was administered by the Montana Department of Fish Wildlife and Parks after the 1988 general hunting season. The population targeted by the questionnaire was those people who had purchased a 1988 deer hunting tag or big-game combination license. An adaptation of Dillman's (1978) Total Design Method was used in conducting the mail survey. Hunters first received the questionnaire booklet (see Appendix A) and cover letter along with a stamped, addressed return envelope. One week later a postcard reminder was sent to those hunters not yet responding. Finally, a second copy of the questionnaire was sent to nonrespondents . Response Rates An initial sample of 5000 questionnaires was mailed to hunters. Residents received 4325 (86.5%) of the surveys and nonresidents 675 (13.5%). This division closely mirrors the actual percentages of resident and nonresident hunters. Of the 5000 questionnaires mailed, 44 were undeliverable and 3328 were completed and returned. This response rate of 66.5% is comparable to other Montana hunting surveys (Loomis, Cooper and Allen, 1988; Brooks, 1988) and is quite acceptable for mail questionnaires. Of the 3328 completed questionnaires, 79 either did not hunt in 1988 or were returned too late to be included in the sample. There was no nonresponse check conducted in this study. It is not possible, therefore, to know if the 33.5% who did not respond differed significantly from the 66.5% who did. The final sample proportions were 18.8% nonresident and 81.2% resident. Since a larger percentage of nonresidents than residents returned questionnaires the nonresident population is slightly overrepresented in the sample. Rather than employ a weighting scheme to increase the resident percentage in the sample all important results are presented for each residency group. CHAPTER IV DESCRIPTIVE STATISTICS The Montana Deer hunting survey contained many questions regarding characteristics of the hunters, the areas in which they hunted, and the last deer hunting trip which they took. The large sample size of this survey allowed the entire sample to be broken down into hunter subgroups and regional subgroups while still retaining large enough sample sizes to ensure meaningful interpretation of both descriptive statistics and economic models . Hunter Characteristics In addition to examining the sample in its entirety the responding hunters were categorized according to two dichotomizations; residents v. nonresidents and guided hunters v. nonguided. Table 1 shows the relationships between these four classifications. Guided hunters in this sample were predominantly a subset of nonresident hunters with roughly 25% of nonresidents employing big game hunting guides. Very few residents (less then 1%) employed guides for their hunts. Table 2 summarizes the similarities and differences between hunters in the four subgroups. While the vast majority of all hunters were male, resident hunters had a lower percentage of males (85.5%) then did nonresidents (94.8%). Nonresidents and guided hunters spent significantly more time hunting deer each year than did residents. Those nonresidents and guided hunters also were twice as likely as the resident and nonguided hunters to belong to a conservation organization. Two characteristics, average age and percent who hunted with rifles, were fairly stable across subgroups. The percentage of hunters who were successful in killing a deer also is relatively stable across groups, but the information in Table 3 suggests some important differences between groups. While 15.9% of residents bagged other big game species on the same trip, the same statistic for nonresidents was 28.3% and for guided hunters 40.7%. These numbers suggest that a significant number of guided hunters in the sample were primarily guided for other species, elk in particular. One final comparison from Table 2 shows that average income varied widely between subgroups. The average income of guided hunters was nearly twice that of resident hunters. This differential would have surely been greater if response categories on the questionnaire had allowed for reporting of incomes in excess of $100,000. Table 1 Montana Deer Hunting Crosstabulation of Residency and Guide Classifications Guided Hunters 164 Nonguided Hunters 2786 Total Hunters 2950 Resident Hunters 2395 Nonresident Hunters 555 Total Hunters 2950 Note: The total population of responding hunters was divided in two manners for analysis. In the first, the total population of 2950 hunters was divided into guided hunters and nonguided hunters, and in the second, the total population of 2950 was divided into residents and nonresidents. Table 2 Montana Deer Hunting Hunter Characteristics Characteristic Residents Nonresidents Guided Nonguided % of all Hunters 81.5 18.5 5.4 94.6 % male 85.5 94.8 94,6 86.7 Average age 37.29 42.10 43.01 37.80 Average Days Per Year Spent Hunting % Belonging to a Conservation Club % Successful in Killing Deer % Rifle Hunters Average Income 10.73 24.4 18.39 55.5 20.12 63.3 11.56 27.9 63.9 68.8 62.7 65.1 93.3 91.3 91.1 93.0 $28,767 $46,385 $56,806 $30,511 Table 3 Montana Deer Hunters Percentage That Killed Other Big Game, by Species Species Residents Nonresidents Guided Nonguided Deer 63.9 68.8 62.7 65.1 Elk 9.2 17.4 27.2 9.6 Antelope 4.9 8.8 11.8 5.3 Bear .2 .5 .5 .3 Other 1.6 1.6 1.2 1.7 Trip Characteristics The trips which the hunters in the four classifications (resident/nonresident and guided/nonguided) took also show many differences. Table 4 shows that while the average number of round trip miles traveled by all hunters was 508, residents averaged 148 miles and nonresidents averaged 2252 miles. Table 4 also shows how the average number of deer seen, hunters seen, and days the trip lasted varied across the hunter subgroups. Nonresidents and guided hunters tended to see more deer on their trips than resident and nonguided hunters. However, those nonresidents also took longer trips which increased the probability of seeing more deer. Therefore, the average number of deer seen per day was relatively stable across groups. It also appears that the degree of perceived hunter congestion was stable across hunter groups with around 20% of each reporting seeing more hunters than they expected. Table 5 is presented in order to compare hunter and trip characteristics across Montana Department of Fish, Wildlife and Parks Administrative Regions. There are significant differences in many of these characteristics. Table 4 Montana Deer Hunting Trip Characteristics Characteristic Residents Nonresidents Guided Nonguided Average Number of Miles Traveled 148 2252 2992 508 % Who Killed Other Big Game 15.9 28.3 40.7 16.9 Average Number of Deer Seen 44.6 78.9 79.9 49.0 Average Number of Days Per Trip 4.49 6.8! 6.56 4.81 Ave. Number of Other Hunters seen 8.9 11.1 7.6 9.38 % Saying Number of Hunters was More than Expected 17.9 20.1 19.9 18.2 Table 5 Montana Deer Hunting Characteristics by Montana DFWP Administrative Region CI laracteristic Region l Reg ion 2 Reg ion 3 Reg ion 4 % Residents 85.0 86.7 31.2 82.9 % Guided 6.0 4.4 5.9 5.7 % Successful 58.6 55.6 53.3 68.6 % that Killed Other Big Game 8.3 19.6 26.9 16.2 # Deer Seen 25.8 27.43 59.12 57.1 # Days Per Trip 5.8 5.31 5.79 4.35 # Hunters Seen 10.05 10.66 13.47 8.51 % Bucks Killed 74.2 79.5 83.2 75.6 Sample Size 440 458 612 637 CI laracteristic Region 5 Region 6 Region 7 % Residents 87.4 85.2 72.2 % Guided 4.9 1.0 7.7 % Successful 75.7 78.1 80.5 % that Killed 0th er Big Game 10.8 24.8 22.1 # Deer Seen 66.4 72.4 58.4 # Days Per Trip 3.47 4.37 4.55 # Hunters Seen 4.63 7.95 6.52 % Bucks Killed 76.7 78.3 79.1 Sample Size 305 289 298 10 Hunter Expenditure Data Resident hunters spent an average of $112.64 for transportation, food, and miscellaneous purchases on their 4.49 day long trips (Table 6). This translates to an expenditure of $25.08 per day. Nonresidents and guided hunters paid substantially more per day for their hunting trips because of the long distances which they traveled, the added necessity for overnight lodging and guide fees. Nonresidents spent $1006.12 per trip or $146.23 per day, and guided hunters spent $1591.95 per trip or $242.67 per day. Finally, hunters in the nonguided subgroup spent $217.47 per trip or $45.21 per day. Table 6 Montana Deer Hunting Trip Expenditures by Hunter Subgroup Average Average Average Average Category Resident Nonresident Guided Nonguided Transportation $ 33.03 $ 308.19 $ 410.67 $ 64.15 Food 30.21 242.57 345.42 56.48 Miscellaneous 49.40 455.36 835.86 96.84 Total 112.64 1006.12 1591.95 217.47 Per Day Expenditures 25.08 146.23 242.67 45.21 11 Hunter Management Preferences Hunters were asked to answer several questions concerning their perception of deer management in Montana. Resident and nonguided hunters were much more likely than nonresidents and nonguided hunters to say that there were too many hunters in their hunting areas (Table 7). Those resident and nonguided hunters who said that there were too many hunters were much less likely than their nonresident, guided counterparts to say that they would accept restrictions on hunting to improve the situation. In general, resident and nonguided hunters felt that a lack of access to hunting areas affected their hunting more than nonresident and guided hunter- did. Summary statistics are also presented for how hunters view the number of bucks in their areas, and what access they believe they should have for game retrieval purposes. 12 Table 7 Montana Deer Hunting Management Preferences by Hunter Subgroup All Res. Nonres, Guide Nonguide (1) % who said there were too many hunters (3) % who said access affects their hunting (4) % who said the number of bucks was GOOD OK POOR 20.4 (2) Of (1) , % who would Accept restrictions 66.3 51.7 22.5 65.5 53.6 9.7 74.2 43.0 11.9 20.8 94.7 65.6 35.5 52.6 26.1 24.8 31.7 37.2 25.4 51.4 52.2 48.6 37.8 52.2 22.5 23.0 19.7 25.0 22.4 (5) of POOR % who would accept restrictions to improve # of bucks (6) % who think these roads should be allowed for game retrieval ONLY OPEN* OPEN AND CLOSED OFF ROAD ALLOWED 71.9 70.8 78. 1 81.5 71.5 47.6 47.6 48.1 58.3 47.2 29.1 29.5 26.9 20.5 29.6 23.2 22.9 24.6 21.1 23.2 ONLY OPEN indicates that respondents believed game retrieval should be allowed only using open roads. OPEN AND CLOSED responses felt game retrieval should be allowed using open and closed roads. OFF ROAD ALLOWED responses felt off-road driving should be allowed for purposes of game retrieval. 13 CHAPTER V MONTANA DEER HUNTING VALUATION ANALYSIS: MODEL SPECIFICATION AND ESTIMATION Contingent Valuation Questions Asked The Montana Deer Hunting Survey asked hunters to answer questions on a number of aspects of their most recent hunting trip. Questions were asked regarding their reasons for hunting and their opinions on the management of hunting areas, as well as questions on demographic and trip characteristics. A copy of the questionnaire is included in Appendix A. For economic modeling purposes, four contingent valuation questions were asked regarding the hunter's most recent trip. The first question asked the hunter to place a value on their most recent hunting trip. This question asked: Suppose that everything about this last hunt was the same except your share of the expenses had been $ X more, would you still have made this trip? The hunter would answer this dichotomous choice CVM question by circling either Yes or No. The dollar amount $ X was one of 10 predetermined bid levels ranging from $ 5 to $ 2000. This amount was varied randomly across questionnaires. Following this question was a set of three dichotomous choice CVM questions presenting hunters with hypothetical changes in their most recent trip and asking them how they would value those changes. These three hypothetical questions were as follows: Imagine that everything about this last trip was the same, except that your chances of bagging a mature buck were twice as great AND your trip costs to visit this site increased by $ X . would you still have made the trip? Imagine everything about this last trip was the same except your chances of killing a doe or small buck were really good and your trip costs increased by $ X . Would you still have made the trip? Now imagine that everything about your last trip was the same except that you would be able to bag an additional deer and your trip costs increased by $_X_, would you still make the hunting trip to this area? The goal of asking these three hypothetical questions was to determine hunters willingness to pay for alternative deer hunting opportunities. As in the current trip question, the dollar amount asked varied between $ 5 and $ 2000 among respondents. 14 Outlier and Protest Responses In the analysis of CVM responses there are two groups of respondents who should be excluded from the sample before any analysis occurs. The first is that group who indicate a willingness to pay the stated bid amount but who would not actually be able to pay that amount given their income. The standard economic definition of demand requires both a willingness and an ability to pay. Therefore those respondents who indicate a willingness but lack the ability to pay the bid amount must be excluded as their response does not meet the constraints of economic theory. Ability to pay was determined by first calculating the percentage of their income which respondents were willing to spend on deer hunting. This was done as follows: PERCENT = ( (TOTAL + BID) * TRIPS ) / INCOME Where: TOTAL = The amount they reported spending on their most recent trip. BID = The dollar bid level asked. TRIPS = The number of separate deer hunting trips they reported taking this season. INCOME= Their reported annual income. This percentage statistic was calculated for each of the four CVM questions. As an initial measure all respondents with a percentage figure greater than 1 were excluded since this group most obviously lacks the ability to pay. The percentages for the remaining respondents were then tabulated for each question giving the following results. PERCENT (Quest. 1) PERCENT (Quest. 2) PERCENT (Quest. 3) PERCENT (Quest. 4) Since the distribution of the calculated variable PERCENT was somewhat skewed rather than distributed normally a three standard deviation confidence interval was placed around the four calculated means in order to determine the cutoff limit for outlier exclusion. In total, 106 observations were eliminated from the following economic analysis due to a reported willingness to pay which exceeded the cutoff limits. The second group of respondents who were excluded from the analysis were those whose responses reflected a "protest" to some aspect of the simulated market. The U.S. Water Resources Council has suggested that a followup question be asked to each CVM 15 Mean Std.Dev. Me an + 3 S.D, N .051 .10 .351 873 .049 ,097 .340 905 .043 .088 .307 605 .044 ,084 .297 749 question. In this survey that question was : "If no, would you have made the trip if your share of the expenses had been only $1 more? Following the "No" response to this question was: "if no, could you briefly explain why not." The responses to these questions were analyzed to develop categories of reasons for responding with a "No". Those hunters who indicated a valid reason for their zero willingness to pay were left in the sample. These valid reasons included: * Respondents who could not afford a higher trip cost. * Respondents saying they would hunt elsewhere if faced with increased trip costs. * Respondents who indicated that the trip would just not be worth any more money. A second group of respondents was excluded from the sample because their reasons indicated they were protesting the market setup rather than legitimately considering the question which was asked. These "protest" responses included: * Respondents saying they didn't understand the questions. * Respondents indicating opposition to any increased taxes, or fees. Specification of the Model Economic theory suggests that certain independent variables be included in estimated equations. These variables are trips, which in this context is a measure of preference, income, and the amount the respondent is asked to pay. Economic theory also suggests that other variables would influence the probability of a respondent answering "yes" to a CVM question. These variables include other variables measuring the tastes and preferences of the respondent, those measuring the quality of the trip, and those measuring the expectations of the respondents. The specification of the logit equation to be estimated is shown in Equation (1). This specification relates the log of the odds of answering yes to a CVM question to a group of explanatory variables chosen by the above economic theory criteria on an a priori basis. (1) ln(P/l-P) = BO - Bl In(BID) +B2 In(INCOME) - B3 In(TRIPS) + B4 In(DRSEEN) - B5 In(HUNTERS) + B6 In(YRSHNT) + B7 (PURPOSE) + B8 (DRKILL) + B9 (CLUB) - BIO In (AGE) 16 Where: P(Y) = Probability of stating a "yes" response. BID = Dollar amount of increased trip cost the hunter was asked to pay. INCOME = Hunter's household income. TRIPS = Number of hunting trips to this area this year. DRSEEN = Number of deer seen on this trip. HUNTERS = Number of other hunters seen on this trip. YRSHNT = Number of years hunter has been hunting deer. PURPOSE = Dummy variable indicating hunting as main purpose of trip. DRKILL = Dummy variable indicating hunter was successful in bagging a deer. CLUB = Dummy variable indicating hunter belongs to a conservation organization. AGE = Age of the hunter. In = Natural log of the previously defined variables. -1 < B3 < 0 This specification, with perhaps the exception of one or two variables, should be valid for the three improved condition CVM questions as well as for the current trip question. Willingness to pay for improvements on the current trip may not be influenced by the number of other hunters seen or by the dummy variable indicating whether the hunter bagged his/her deer. It may be noted that in Equation (1) all independent variables (except dummy variables) are logged. Previous applications have shown that this double-log model generally provides a better fit to dichotomous choice data 17 Estimated Equations Using the data from the Montana DFWP deer Hunting Survey, equations were estimated for the entire sample as well as each of the aggregated subgroups. The hunter subgroups were residents, nonresidents, guided hunters and nonguided hunters. Each of these groups had models estimated for current conditions, for doubling chances of bagging a large buck, for a very good chance of bagging a doe or small buck and for the chance to bag a second deer. Tables 8-11 show the estimated models for the current conditions question as well as the three hypothetical questions. Table 8 shows the estimated equation for the probability of paying an increase in hunting costs for the current hunting conditions. All of the included variables for these equations are significant at the 90% level with most being significant at the 95 or 99% level. All variables with the exception of LHUNTERS and PURPOSE have the expected signs. Loomis, Cooper and Allen (1988) also found that the coefficient on LHUNTERS was consistently the opposite of what would be expected for a congestion variable. Perhaps this indicates that in the case of big game hunting in Montana, congestion is correlated with other positive aspects of the hunting experience. The PURPOSE dummy variable was expected to return a positive sign, indicating that those whose main purpose for taking the trip was to hunt would value the experience more highly. In the models where PURPOSE was significant, the opposite was true. This indicates that either the investigators a priori expectations about this variable were wrong or that the variable is measuring something other than was intended. Table 9 shows the estimated models for the probability of paying a higher trip cost for doubling the hunters chances of bagging a mature buck. All of the entered variables in this model are significant to the 95% level and all have the expected signs with the exceptions noted above of LHUNTERS and PURPOSE. Table 10 presents the estimates for the model which determines the probability of paying a higher trip cost for having a very good chance of bagging a doe or a small buck. The included variables are all significant at the 90% level, and all excepting PURPOSE and LHUNTERS have the expected sign. Finally, Table 11 shows the estimated models for the probability of paying a higher trip cost for a chance of getting an extra deer. All included variables in these models are significant at the 95% level and all excluding LHUNTERS and PURPOSE have the expected sign. Table 8 Montana Deer Hunting Current Trip, Estimation by Hunter Group Entire Variable Sample Residents Nonres. Guided Nonguided Constant 1.009 3.8378 -3.5533 -4.2878 2.2360 (T-Stats) (1.43) (15.61) (-1.98) (-1.14) (2.77) LBIDTRIP -.8868 -.9277 -.9321 -1.0049 .8916 (-24.02) (-22.29) (-9.22) (-4.98) (-23.56) LINCOME .2506 — .8485 .09525 .1661 (3.36) (4.81) (2.71) (2.15) LTRIPS -.3012 -.1200 — -.2459 (-5.03) (-1.75) (-3.99) LDRSEEN .1031 .0739 — — .1178 (4.12) (2.56) (4.37) LHUNTERS .0212 .0370 .0337 (2.09) (3.05) (3.10) LYRSHNT .1085 (1.99) — — — — PURPOSE — -.1890 (-1.94) — — -.1608 (-1.87) DRKILL — .1227 (1.82) — — — CLUB .2730 .1867 .2753 (4.78) (2.70) (4.60) LAGE Sample Size 2534 2054 462 146 2381 19 Table 9 Montana Deer Hunting Double Chance of Buck, Estimation by Hunter Group Entire Variable Sample Residents Nonres. Guided Nonguided Constant 3.4439 5.3863 - 4.226 9.7235 2.7097 (T-Stats) (13.05) (7.90) (-2.05) (5.43) (2.80) LBIDTRIP -.9153 -.9005 -1.2513 -1.0049 -.9179 (-24.56) (-22.90) (-10.06) (-4.98) (-24.44) LINCOME .3140 — 1.0107 -- .2854 (3.36) (4.95) (3.55) LTRIPS -.2619 -.1200 — -3.297 -.1943 (-4.30) (-1.75) (-3.24) (-3.14) LDRSEEN . 1166 .0965 .1229 (3.89) (3.19) (4.11) LHUNTERS ~ ~ ~ — ~ LYRSHNT — .2045 (2.22) ~ — .2440 (2.83) PURPOSE — — ~ — — DRKILL ~ — — — ~ CLUB .3258 .2098 .3553 __ .2525 (5.64) (3.10) (2.75) (4.18) LAGE — -.6584 (-3.00) — — -.6924 (-3.35) Sample Size 2454 2060 464 145 2391 20 Table 10 Montana Deer Hunting Good Chance of Doe, Estimation by Hunter Group Entire Variable Sample Residents Nonres. Guided Nonguided Constant 3.0805 3.2303 4.6240 .7853 3.1833 (T-Stats) (14.25) (14.16) (2.79) (1.469) (3.20) LBIDTRIP -.8356 -.8838 -.6564 -.3315 -.8700 (-23.5) (-21.6) (-9.58) (-3.23) (-23.39) LINCOME ~ — ~ ~ ~ LTRIPS -.2703 -.1851 __ ._ -.2422 (-4.10) (-2.47) (-3.56) LDRSEEN .0496 (1.74) — — — .0551 (1.83) LHUNTERS — .0248 (1.92) — — .0210 (1.77) LYRSHNT ~ — ~ — ~ PURPOSE -.2164 -.2055 __ __ -.2470 (-2.31) (-1.96) (-2.63) DRKILL ~ ~ ~ — — CLUB .1863 .1275 .2113 „ .1814 (2.99) (1.72) (1.76) (2.79) LAGE — — -1.034 (-1.96) — — Sample Size 2447 2055 459 140 2383 21 Table 11 Montana Deer Hunting Chance of Extra Deer, Estimation by Hunter Group Entire Variable Sample Residents Nonres. Guided Nonguided Constant 5.1176 5.5852 -2.2527 4.5345 3.1171 (T-Stats) (8.61) (9.00) (-1.11) (5.30) (3.20) LBIDTRIP -.9883 -.9844 -1.0477 -.8278 -.9959 (-24.82) (-22/70) (-10.65) (-5.35) (-24.51) LINCOME .3331 — .6460 -- .2691 (3.20) (3.30) (3.06) LTRIPS -.2400 -- — -2.07 -.1803 (-3.61) (-2.11) (-2.69) LDRSEEN .0855 .1767 _- .0695 (3.04) (2.46) (2.48) LHUNTERS — ~ ~ ~ — LYRSHNT ~ ~ ~ — — PURPOSE -.2858 -.3257 __ -.3002 (-2.95) (-3.04) (-3.11) DRKILL ~ — ~ ~ ~ CLUB .2783 .1776 .3237 __ .2594 (4.40) (2.38) (2.55) (3.94) LAGE -.4180 -.4612 — -.4705 (-2.80) (-2.95) (-3.13) Sample Size 2425 2037 457 143 2360 22 Benefit Estimates Three alternative measures of willingness to pay are presented for the deer data. The mathematical expectation (mean) of maximum willingness to pay is first presented and is labeled MEAN-LOGIT. The bivariate forms of the estimated equations (showing the probability of a "yes" response as a function of the bid amount) can be graphed with the probability of acceptance on the vertical axis and the bid amount on the horizontal axis. This graphing shows a high probability of acceptance at low bid amounts. This probability declines and asymptotically approaches zero at high bid amounts. The MEAN-LOGIT is obtained by integrating the logit function from a bid level of zero to some upper limit. The mean of the logit corresponds to the area under the two dimensional curve and thus it can be intuitively interpreted as the probability of a "yes" times the bid amount. In this study the models were estimated using a bivariate specification and the MEAN-LOGIT calculation was based upon this bivariate form (the bivariate specifications of all models used in this study are shown in Appendix B) . The upper limit of integration to be used in the MEAN-LOGIT calculation is the uppermost bid level asked, or $2000. While there is no clear basis for choosing an upper limit of integration it is inappropriate on statistical grounds to extrapolate beyond the range of the sample data (in this case $2000). The second measure of willingness to pay presented here is the median of the distribution (labeled MEDIAN) . The median is simply the point where the probability of acceptance equals .5. Solving the bivariate estimates of the equations for P=.5 yields a median which is equal to the antilog of the calculated intercept over the slope coefficient on bids. A final measure of willingness to pay is calculated using a nonparametric estimation technique suggested by Duffield and Patterson (1990) . As stated before, the mean of the logit can be intuitively interpreted as the probability of a "yes" times the bid amount. The nonparametric technique explicitly calculates this mean from the bid levels and the responses to those levels. The use of this nonparametric technique sidesteps a constraint of the logit mean by allowing the calculation of a sample variance and hence the construction of confidence intervals around the calculated mean. Table 12 shows willingness to pay for each of the three measures (MEAN-LOGIT, MEDIAN, and NONPARAMETRIC) for the current conditions question. These statistics are reported for the entire sample as well as for each of the four hunter subgroups. Although there are significant differences between hunter subgroups, it appears that the surveyed trips are relatively valuable to all hunters. It is interesting to note that the estimated MEAN-LOGIT and the calculated NONPARAMETRIC mean are 23 Table 12 Montana Deer Study State Average Net Economic Values Per Trip and Per Hunter Day Current Trip Question PER TRIP VALUES: Method State Residents Nonres, Guided Nonguided 799.99 269.05 486.21 65.01 785.45 281.87 MEAN-LOGIT $ 301.51 208.74 705.85 MEDIAN $ 72.97 52.14 343,30 NONPARAMETRIC $ 311.34 229.20 652.17 PER DAY VALUES; Method State Residents Nonres, Guided Nonguided 122.02 55.81 74.16 13.49 119.81 58.48 MEAN-LOGIT $ 61.40 MEDIAN $ 14.86 NONPARAMETRIC $ 6 3.41 46. .48 102. .44 11. .61 49. ,82 51. .04 94, .65 24 consistently quite close. It is not surprising that the guided and nonresident hunters whose average incomes were substantially greater than those of the resident and nonguided group placed a substantially higher value on their hunting experiences. Following the willingness to pay statistics are the per hunter day valuations for each of the three methods. Again, allowing for the longer average length of trip for the nonresident and guided hunters there is a substantial difference between the values which they place on the experience and those of the resident and nonguided subgroups. As in many other studies, the estimated median values are much lower than the estimated mean values. This indicates that the distribution of willingness to pay is skewed with a greater proportion of individuals being willing to pay high values (compared to a normal bell-shaped curve) . The median indicates the minimum amount that at least 50 percent of the population would be willing to pay. However, for purposes of aggregation (such as estimating the total benefits of Montana deer hunting) the mean is the correct measure. See Duffield and Patterson (1990) for further discussion regarding choice of welfare measures. Analysis of Values Across CVM Questions One of the major objectives of the Montana DFWP Deer Hunting Survey was to estimate net economic values for the current trip under three scenarios of hypothetically improved conditions. Specifically, these improvements were (1) doubling the hunters chance of bagging a mature buck, (2) increasing the hunters chances of bagging a doe or small buck, and (3) allowing the hunter to bag an extra deer on his/her trip. The results of the economic analysis of these three questions (presented in Table 14) proved to be unexpected and somewhat problematic. The problems did not stem from a qualitative interpretation of values returned, but rather from their magnitudes. Table 13 shows that per trip net economic values were very consistent in their ranking across questions. Doubling chances for a mature buck was valued highest, the chance for an extra deer was valued slightly lower, and a good chance for a doe or small buck was valued significantly below both. The consistency of these responses suggests that Montana deer hunters place very different values on alternative deer hunting experiences. This is consistent with the investigators expectations. What is, however, unexpected is that nearly all of the improved condition questions returned net economic values which were lower than for the current conditions question. There are two possible reasons for this. First, this may simply indicate that Montana deer hunters are, on a whole, satisfied with current hunting conditions and do not view the improved condition scenarios as important to their enjoyment of the current trip. While it is likely that this type of hunter satisfaction plays a role in explaining the differences between 25 Table 13 Montana Deer Hunting Net Economic Values Per Trip Improved Condition Scenarios PER TRIP VALUES: DOUBLE CHANCE OF MATURE BUCK Method State Resident Nonres. Guided Nonguided MEAN-LOGIT $ 260.92 202.50 490.72 618.00 235.30 MEDIAN $ 69.70 51.06 224.96 379.40 60.75 NONPARAMETRIC $ 262.75 213.89 465.96 566.80 243.19 GOOD CHANCE OF DOE OR SMALL BUCK Method State Resident Nonres, Guided Nonguided 419.77 140.06 20.94 25.38 332.18 147.25 MEAN-LOGIT $ 154.06 123.41 302.11 MEDIAN $ 25.22 23.41 37.76 NONPARAMETRIC $ 157.76 129.39 281.88 CHANCE OF AN EXTRA DEER Method State Resident Nonres, Guided Nonguided 600.55 176.89 231.49 45.02 639.84 190.90 MEAN-LOGIT $ 197.61 150.66 406.56 MEDIAN $ 49.08 37.06 153.95 NONPARAMETRIC $ 214.36 166.10 427.08 26 the current and improved conditions trip values, the values might also be influenced by responses from hunters who were hunting other species in addition to deer. While the Montana Deer Hunting Survey effectively identified those hunters whose trip was made primarily for the purpose of hunting, the distinction was not made between those primarily hunting deer and those who might primarily be hunting elk or another big game species while at the same time be willing to shoot a deer if the opportunity arose. Respondents were explicitly asked (see section II and Appendix A) about "your last deer hunting trip", and over 60 percent of respondents did bag a deer; however, this does not preclude the possibility that elk were the primary objective of the hunting trip. Two statistics from the survey data give credence to the possibility that a substantial number of elk hunters were included in the survey. The average number of days which resident hunters report having spent on their most recent trip is more than double the number of days per trip found in a previous DFWP deer study (Brooks 1988) . Brooks found that resident hunters spend an average of 1.98 days per trip hunting deer. This makes intuitive sense since a large number of residents engage in only day or weekend deer hunts. The average number of resident days found in this study was 4.49 suggesting that a substantial number of these trips were made for the purpose of hunting elk which generally requires a larger commitment of time and energy and is taken somewhat more seriously by hunters. This difference may also be in part because Brooks (1988) was based on a telephone survey where a list of all hunting trips for the season was obtained from the respondent. The detailed trip information was then asked about one specific trip selected at random. In this study (as in Loomis, Cooper and Allen (1988)), the constraints of using a mail survey required that the specific trip selected for detailed information was the "most recent" or "last" hunting trip. The last hunting trip is more likely to have been a successful trip (and success is in part a function of the length of the trip) . This may also in part explain the difference in days per trip between Brooks (1988) and the current study. Nonresidents in Brooks' study spent an average of 6.32 days per trip compared to 6.89 days in this study. There is reason to believe that the number of days nonresident deer and elk hunters spend on their trips is relatively equal. Nonresidents, particularly those who are also guided, tend to commit a week to hunting Montana regardless of the species they are hunting (the possible exceptions are those nonresidents living near their desired hunt areas) . More indicative of a possible "elk hunter bias" in the sample is the statistic showing the percentage of each hunter subgroup to bag an elk on their most recent trip. The data showed that 9.2% 27 of resident hunters reported bagging an elk on their trip. Statewide the success rate in recent years for elk hunters is approximately 19%, This suggests that a significant proportion of responding resident hunters were on trips where elk hunting was at least as important as deer hunting. As was reported previously, over 27% of guided hunters in the sample bagged elk on their trip. This indicates that a majority of these hunters were being primarily guided for elk. Even if we conclude that a large number of elk hunters were included in the deer survey responses, interpretation of the magnitudes of the improved conditions values remains problematic. This conclusion, however, would make possible an explanation which has intuitive appeal, even though it lacks strict quantitative rigor. If the net economic values for the current trip estimation were influenced by elk hunters the improved condition questions (which dealt exclusively with improvements in deer hunting conditions) might have been viewed as relatively unimportant in the context of their elk hunting trip. The values which they placed on these improvements might therefore have been discounted. With hindsight, it would have been advisable to ask respondents what species was the primary objective of their hunt. Analysis of Values Across Regions In addition to the models estimated for the entire state and for the four hunter subgroups, models were estimated for each of the seven DFWP administrative regions. Table 14 shows that there is relative stability of values across the regions for the four CVM questions. Indeed, an analysis of confidence intervals calculated for the nonparametric mean show that no statistical difference between regions exists at the 95% level of confidence. As was the case for the entire sample and for the hunter subgroup samples the net economic values for the three improved conditions questions were consistently ranked, but consistently lower than for the current conditions question. While the values for the seven regions still show the disparity between the current trip values and the improved conditions values that was discussed above, they also provide support for the magnitudes of the values as applied to deer hunting. Of particular interest are the values for regions 6 and 7. In 1989 the total elk harvest for regions 6 and 7 were 299 and 40, respectively. With such a low harvest of elk, it seems certain that "elk hunter bias" did not play a role in inflating the net economic values of deer hunting from these regions. Region 7, with the lowest incidence of elk hunting, nevertheless, shows the highest values for the current trip question. 28 Analysis of Dispersion Around Nonparametric Means As was mentioned previously, a nonparametric mean suggested by Duffield and Patterson (1989) was calculated for each of the estimated equations. The use of this nonparametric technique allowed the calculation of a sample variance and thus the construction of confidence intervals around the calculated means, A comparison of the estimated logit means and the nonparametric means shows them to be quite close in most cases. Table 15 shows the nonparametric means and 95% confidence intervals for each of the four CVM questions for the entire sample and the four hunter subgroups. An analysis of these figures shows significant variation between hunter subgroup as well as between certain improved conditions values. Table 16 shows the same calculated statistics for each of the seven Montana DFWP administrative regions. As was mentioned before, an analysis of the 95% confidence intervals surrounding the nonparametric means for the seven regions shows no significant difference in net economic value for deer hunting experiences. 29 Table 14 Montana Deer Study Montana Deer Hunting Values by Region Region 1 Current Mature Doe or Extra Condition Buck Small Buck Deer Constant 4.1367 4.0176 2.3179 3.6616 BID Coeff. -.9616 -.9397 -.7739 -.9523 MEAN-LOGIT 258.41 223.68 151.90 190.07 MEDIAN 73.84 61.59 19.98 46.75 NONPARAMETRIC 314.75 253.41 153.36 235.53 Region 2 Current Mature Doe or Extra Condition Buck Small Buck Deer Constant 3.1894 3.7862 2.6712 3.2505 BID Coeff. -.7858 -.9397 -.8637 -.9361 MEAN-LOGIT 284.16 220.49 131.99 149.48 MEDIAN 57.90 56.21 22.03 32.21 NONPARAMETRIC 269.47 206.17 123.28 175.33 Region 3 Current Mature Doe or Extra Condition Buck Small Buck Deer Constant 3.2487 3.5068 2.9427 3.1222 BID Coeff. -.7565 -.8425 -.8566 -.8205 MEAN-LOGIT 339.77 277.48 169.13 229.90 MEDIAN 73.28 64.22 31.04 44.93 NONPARAMETRIC 340.92 265.77 187.89 237.36 30 Table 14 Cont. Montana Deer Study Montana Deer Hunting Values by Region Region 4 Current Mature Doe or Extra Condition Buck Small Buck Deer Constant 3.8784 4.3255 2.9932 3.9715 BID Coeff. -.8913 -1.038 -.8896 -.9929 MEAN-LOGIT 292.30 212.68 151.11 200.08 MEDIAN 77.58 64.45 17.37 54.59 NONPARAMETRIC 300.73 203.41 164.56 218.68 Reaion 5 Current Mature Doe or Extra Condition Buck Small Buck Deer Constant 3.5708 3.4922 2.1143 4.0298 BID Coeff. -.8749 -.8314 -.7405 -1.086 MEAN-LOGIT 251.24 288.70 151.30 140.21 MEDIAN 59.23 66.71 17.37 40.82 NONPARAMETRIC 264.39 280.38 150.48 141.53 Region 6 Current Mature Doe or Extra Condition Buck Small Buck Deer Constant 4.6196 4.0181 3.2964 4.4245 BID Coeff. -1.018 -.8939 -.9291 -1.047 MEAN-LOGIT 285.11 319.26 159.81 220.13 MEDIAN 93.53 89.57 34.74 68.49 NONPARAMETRIC 322.45 332.27 150.83 246.00 31 Table 14 Cont. Montana Deer Study Montana Deer Hunting Values by Region Current Mature Doe or Extra Condition Buck Small Buck Deer Reaion 7 Mature Doe or Buck Small Buck 4.5389 2.4954 -.9771 -.8215 320.54 139.70 104.09 20.85 350.32 162.00 Constant 3.2246 4.5389 2.4954 4.3207 BID Coeff. -.7229 -.9771 -.8215 -.9899 MEAN-LOGIT 389.09 320.54 139.70 260.65 MEDIAN 86.54 104.09 20.85 78.63 NONPARAMETRIC 343.18 350.32 162.00 256.21 32 Table 15 Montana Deer Hunting Nonparametrlc Means and Confidence Intervals CURRENT TRIP QUESTION Sample Mean Lower C.I. Upper C.I, Entire Sample Residents Nonresidents Guided Nonguided $ 311.34 229.20 652.17 785.45 281.87 $ 281.43 200.27 558.98 606.21 252.53 $ 341.25 258. 14 745. 35 964.69 311.21 DOUBLE CHANCE OF MATURE BUCK Sample Mean Lower C.I. Upper C.I Entire Sample Residents Nonresidents Guided Nonguided $ 262.75 213.89 465.96 566.80 243.19 $ 235.79 185.92 394.59 444.45 215.98 $ 289.71 241.86 537.33 689.15 270.39 Calculated confidence intervals are set at the 95% level of confidence . 33 Table 15 Cont. Montana Deer Hunting Nonparametrlc Means and Confidence Intervals GOOD CHANCE OF DOE OR SMALL BUCK Sample Mean Lower C.I. Upper C.I. Entire Sample Residents Nonresidents Guided Nonguided $ 157.76 129.39 281.88 332. 18 147.25 $ 136.52 108.43 216.04 204.03 126.13 $ 179.00 150.35 347.73 460.33 168.37 CHANCE OF AN EXTRA DEER Sample Mean Lower C.I. Upper C.I Entire Sample Residents Nonresidents Guided Nonguided $ 214.36 166.10 427.08 639.84 190.90 $ 188.45 141.27 341.35 427.91 166.42 $ 240.27 190.92 512.82 851.77 215.38 34 Table 16 Montana Deer Hunting Nonparametric Means and Confidence Intervals CURRENT TRIP QUESTION Region Mean Lower C.I. Upper C.I. $ 314.75 269.47 340.92 300.73 264.39 322.45 343.18 $ 224.08 199.34 272.05 238.48 171.83 216. 14 259.32 $ 405.41 339,59 409.79 362.98 356.96 428.75 427.03 DOUBLE CHANCE OF A MATURE BUCK Region Mean Lower C.I. Upper C.I $ 253.41 206.17 265.77 203.41 280.38 332.27 350.32 $ 179.93 149.49 205.30 157.88 189.63 223.16 248.98 $ 326.89 262.84 326.24 248.94 371. 12 441.38 451.67 35 Table 16 Cont. Montana Deer Hunting Nonparametric Means and Confidence Intervals GOOD CHANCE OF DOE OR SMALL BUCK Region Mean Lower C.I. Upper C.I, $ 153.36 123.38 187.89 164.56 150.48 150.83 162.00 $ 92.91 81.51 129.39 116.16 87.02 96.59 85.92 $ 213.81 165.06 246.40 212.96 213.94 205.06 238.08 CHANCE OF AN EXTRA DEER Region Mean Lower C.I. Upper C.I, $ 235.53 175.33 237.36 218.68 141.53 246.00 256.21 $ 152.97 110.05 174.71 162.07 91.03 143.31 170. 16 $ 318.09 240.60 300.02 275.29 192.04 348.71 342.26 36 Comparison of Results to Previous Studies The results of this study can be compared to several other Montana big game hunting studies. Since questions remain as to whether this study was successful in isolating only deer hunters in its sampling process, comparisons will be made with previous elk hunting studies as well as those for deer hunting. Brooks (1988) undertook a travel cost model analysis of Montana deer hunting (see Dwyer, Kelly and Bowes (1977) for a discussion of travel cost methodology) . His study was based on a sample of 1,031 Montana deer hunting license holders and used a reported cost of 37 cents per mile in the calculation of net economic values. Brooks found a per trip value for Montana deer hunting of $ 108.00, and a per day value of $ 54.94. Also in 1988 Duffield undertook another TCM study of Montana elk hunting as a companion to Brooks' deer study. Duffield 's study was based on a sample of 553 hunters whose main purpose was elk hunting. This study, which utilized a reported cost of 42.2 cents per mile found that the average Montana elk hunting trip has a net economic value of $ 184.56 per trip or $ 65.58 per day. Loomis, Cooper, and Allen (1988) studied Montana elk hunting using both open ended CVM and dichotomous choice CVM methodology. Using a sample size of 5,000 Montana elk hunting license holders they found a per trip mean net economic value of $ 262.31 for the dichotomous choice question, $ 93.61 for the open ended CVM question and $ 72.27 for the median of the dichotomous choice responses. These values translate into per day values of $ 39.90 for the mean logit, $14.24 for the mean open ended CVM and $ 10.99 for the median logit. Loomis et al . used an upper integration limit of $ 1100 for the calculation of their mean logit values. Loomis, Creel and Cooper (1989) conducted a study of the economic value of deer hunting in California using a dichotomous choice CVM methodology and found a statewide average net economic value of $ 191.45 per trip, or $68.73 per day. Table 17 shows a comparison of the current studies results with those of the studies mentioned above. Each studies values are reported in the study years dollars so com.parison across studies must be made with care. A comparison of the per day values of Table 17 show that the current study values are comparable to the results of other deer hunting valuation studies. The per day comparison is more appropriate given the difference in days per trip across studies as discussed previously. This lends a degree of validation to the magnitudes of the values reported here. It should be noted that the benefit estimates for the contingent 37 valuation models are sensitive to the upper limit of integration. The upper limit for the two Montana CVM studies were based on the maximum bid amount asked : $1100 for Loomis et al . (1988) on elk and $2000 for the current study on deer. When the Loomis et al . (1988) is extrapolated to a $2000 integration limit and corrected for inflation, the per day value is very similar to the results of the current study. The maximum bid amount was increased to $2000 for the current study because of the relatively high proportion of respondents who were willing to pay up to $1100 in the previous surveys. 38 Table 17 Montana Deer Hunting Comparison of Results With Previous Big Game Studies Value Per Trip Value Per Day Method / Study (Study Year Dollars) Travel Cost Method Duffield (1988) Elk $ 184.56 $ 65.58 Brooks (1988) Deer $ 108.00 $ 54.94 Contingent Valuation Method Loomis et al. (1988) Elk $ 262.31 $ 39.90 Current Study Deer ($2000 integration limit) $ 301.51 $ 61.40 Loomis et ai.(1989) Deer $ 191.45 $ 68.73 Note:l) For travel cost models, the cents per mile factor was: Duffield (1988) 42.2 cents/mile reported cost. Brooks (1988) 37 cents/mile reported cost. 2) Note that Loomis et al . (1989) is for deer hunting in California, all other studies are for Montana hunting experiences . 3) For the contingent valuation models, the benefits are sensitive to the upper limit of integration. Loomis et al . (1988) used a $1100 upper limit of integration because this was the highest bid amount asked. In the current study, the maximum bid amount was $2000. Results for Loomis et al . (1988) when extrapolated to a $2000 bid limit and corrected for inflation are nearly identical to the current studies per day values. 39 40 CHAPTER VI MARKET SEGMENTATION: CLUSTER ANALYSIS OF HUNTER TYPES Marlcet Segmentation The mean net economic values presented thus far are useful in gaining an understanding of how the average deer hunter values his/her recreational experiences. Further, the values which hunter subgroups place on their trips illuminate differences across such things as residency and guided, nonguided status. Useful as these groupings are, they nevertheless mask very real differences and similarities between hunters and their motivations for and expectations about hunting. There is no truly average deer hunter, and even though such subgroups as guided hunters share many of the same motivations, the term "average guided hunter" remains a statistical construct of questionable meaning. Individuals hunt for personal reasons, but this does not preclude many individuals from sharing similar reasons for hunting. As pointed out by Allen (1987), research suggests that there are several methods available for identifying different "types" of hunters within a sample. By identifying what "type" a hunter is it becomes possible to attach dollar values not just to deer hunting but to various types of deer hunting experiences. Cluster Analysis Design The cluster analysis used in this study was meant to isolate subgroups, or "types", of deer hunters who defined their hunting experience similarly. By understanding their collective motivations for hunting we are better able to understand the basis upon which they value their experiences. Cluster analysis attempts to define subgroups of hunters which have significantly different, yet conceptually meaningful characteristics. The application of clustering used in this study follows closely that suggested by Allen (1988) in his cluster analysis of Montana elk hunters. The Montana deer hunting data had a large number of cases (in excess of 2500) and therefore the SPSSx Quick Cluster program, which efficiently clusters large files, was used. This program sorts cases based on their Euclidean distance from cluster centers which have been chosen from well distanced cases. The clustering was performed on eight questions which asked hunters to rate in importance reasons for hunting and factors which influenced where they decided to hunt. These questions were 41 chosen a priori as the most efficient variables in identifying distinct hunter types. Reasons which a majority of hunters rated similarly were not used in the clustering since these variables provide little help in drawing distinctions between hunter groups . The SPSSx Quick Cluster program does not select a specific number of clusters statistically. The programmer must pick the desired number. Allen (1988) discussed three criteria for determining the optimal number of clusters. (1) The number of observations in each cluster must be large enough to allow economic analysis (about 100 observations) . (2) The clusters should be different enough to define distinct hunter subgroups, yet they must conceptually make sense. (3) The smallest number of clusters which does not mask important differences between types of hunters is preferred. Both in his study of Montana anglers (1987) and that of Montana elk hunters (1988) Allen chose to use four clusters for grouping recreationists. For this study, clusters of 2 , 3, 4, and 5 were run and since sample size criteria were met in all cases an optimal number of clusters was first selected based on maximum average distance between cluster centers. This basis also yielded a cluster size of four. These clusters were then analyzed to determine whether the groupings made conceptual sense. It was found that two of the four hunter groupings were very distinct and easily labeled. These were Meat Hunters and Trophy Hunters. Two questions which asked respondents to rank the importance of taking a trophy deer were included in the clustering process. Respondents consistently ranked these two questions similarly. This suggests that respondents took the clustering questions seriously. Meat Hunters and Trophy Hunters responded in opposite ways to the trophy and meat questions making their basic motivations easy to identify. The remaining two clusters could perhaps best be termed as two Generalist types of hunters. One cluster which we termed the Generalist-Enthusiast ranked the importance of all reasons for hunting highly. This group seemed motivated by nearly all aspects of the hunt (meat, trophies, testing skills, easy access) . The second Generalist class which we termed the Generalist-Meat hunter seemed most motivated by good access to the hunt and the fact that they had a special permit to hunt an area. Besides these factors they ranked meat as a major motivation and trophies as relatively unimportant. One source of validation for the clustering process lies in examining how the different cluster groups compare in regard to characteristics not used in the clustering process. If the clusters were indeed distinct subgroups we would expect that 42 differences would exist between the groups in many areas. Our Table 18 Montana Deer Hunting Comparison of Hunter Characteristics Across Clusters CLUSTER 1 2 3 4 Total dollars spent on hunting trip $ 238.73 95.65 239.85 610.19 Average income $ 30,151 27,043 32,784 41,421 Percent hunting on guided trips 4.2 % 1.0 % 2.2 % 14.6 % Percent who rate hunting as their favorite activity 13.4 % 8.4 % 9.1 % 20.6 % Percent who belong to a sportsmans organization 31.3 % 20.7 % 32.9 % 44.6 % Note: Cluster 1 = Generalist-Enthusiast Hunter Cluster 2 = Meat Hunter Cluster 3 = Generalist-Meat Hunter Cluster 4 = Trophy Hunter 43 analysis showed significant variation between clusters on several of the characteristics which we examined. Table 18 shows how clusters compare across several hunter characteristics. Description of Hunter Types Generalist-Enthusiast Hunters These hunters seemed to enjoy nearly every aspect of the deer hunting trip. The three highest rated reasons which they gave for hunting were "for the meat", "for a chance at a big trophy", and "to test my hunting skills". Lowest of importance to this group was having a special permit to hunt an area . Meat Hunters Hunters in this cluster seemed most interested in "getting in the meat", and doing this as cheaply and easily as possible. These hunters rated hunting for the meat as their most important motivation and hunting close to home as second in importance. Table 19 shows that on the average this group spent less than half of what the two generalist clusters spent on their trips and less than one sixth what Trophy Hunters spent. This supports the suggestion that this group views meat as a major goal of their trips. Meat Hunters rate hunting for trophies and permit hunting as of low importance . Generalist-Meat Hunters This group seems to be somewhat opportunistic in their reasons for hunting. The two highest rated reasons given by this group were good road access to the area and because they had a special permit to hunt the area. Also important to this group was hunting for meat. The Generalist-Meat Hunters rated distance from home and trophy hunting as their least important motivations for taking the trip. Trophy Hunters These hunters were most interested in bagging a trophy buck and testing their skills along the way. This was the only group of hunters to rate bagging a trophy as more important than hunting for meat. Access, hunting close to home, and having a special permit were all relatively unimportant to this group. Economic Analysis of Cluster Groupings The SPSSx clustering procedure attaches a variable to each observation which indicates to which cluster it belongs. The sample sizes of the final cluster groupings were as follows: Generalist-Enthusiast = 699 (27%), Meat Hunters = 923 (35.6%), Generalist-Meat Hunters = 363 (14%) and Trophy Hunters = 606 (23.4%). It must be pointed out that the resulting cluster sizes and types are highly dependent on the selection of variables used in the clustering process. To regroup the hunters using different variables or different data would no doubt change the 44 cluster makeup. Multivariate logit equations were estimated for each of the four clusters as well as for each of the CVM questions. Tables 19-22 present the results of these estimations. Table 19 shows the estimated equations for the current conditions CVM question. All included variables in the estimated equations are significant at the 95% level of confidence. Additionally, with the exception of LHUNTER, all have the expected sign. the coefficient on LTRIPS, where included in the models, meets the requirements necessary for consistency with economic theory. The equations for the "double chance of a large buck" models are shown in table 20. All included variables in those models are significant at the 90% level with most significant at the 95% level. With the exception of the dummy variable PURPOSE all show the expected signs. Table 21 shows the estimated models for the "good chance of a doe or small buck" CVM question. Fewer variables were significant in these models. The ones that were, with the exception of PURPOSE, showed significance at the 90% level and with the exception again of PURPOSE had the expected signs. The estimated equations for the final CVM question "chance of an extra deer" are shown in Table 22. Again, all variables are significant at the 90% level or higher and all except PURPOSE have the expected signs. The bivariate forms of these logit equations were also estimated and net economic values were calculated as the LOGIT-MEANs and MEDIAN statistics (Table 23) . The hunters in different clusters placed very different values on the Montana deer hunting experience. Trophy hunters value their trips the highest with a MEAN-LOGIT value of $ 470.70 for the current trip estimation. On the other end of the spectrum are the Meat hunters who value their current trip at only $ 181.92. The values of the remaining two hunter groups fall between these two figures. As was found with the other aggregation schemes, respondents consistently placed a lower value on the improved condition questions than on the current trip question. As was discussed before, this may be indicative of an "elk hunter bias" in the sample responses. 45 Table 19 Montana Deer Hunting Current Trip Estimation by Cluster Variable Enthusiast Meat Genrl.-Meat Trophy Constant 3.7650 3.5914 3.5512 .3644 (T-Stats) (8.34) (10.43) (5.53) (.209) LBIDTRIP -.8647 -.9258 -.9129 -.8654 (-11.64) (-13.39) (-8.06) (-10.53) LINCOME — — — .4021 (2.47) LTRIPS -.3423 (-2.82) ~ — -.3867 (-2.98) LDRSEEN .1450 (2.36) — .1873 (2.08) — LHUNTERS — .0449 (2.25) — — LYRSHNT PURPOSE DRKILL .2446 (2.24) CLUB .3832 (3.30) ~ .2781 (2.49) .2726 (2.46) LAGE Sample Size 583 743 300 523 46 Table 20 Montana Deer Hunting Double Chance of Buck Estimation by Cluster Variable Enthusiast Meat Genrl.-Meat Trophy Constant 4.5708 3.7246 3.0443 -1.1089 (T-Stats) (9.94) (9.74) (4.61) (-.586) LBIDTRIP -.8953 -.9710 -.8733 -1.1152 (-12.01) (-13.79) (-8.06) (-10.53) LINCOME — — — .6902 (3.79) LTRIPS -.2166 -.2339 -.3461 -.2828 (-1.88) (-1.95) (-1.73) (-2.10) LDRSEEN — .1024 (2.15) .2384 (1.97) — LHUNTERS — — — — LYRSHNT ~ ~ — ~ PURPOSE -.4295 (-2.15) — — — DRKILL CLUB — .2362 (1.93) LAGE .2637 (2.24) .3142 (2.67) Sample Size 586 748 300 523 47 Table 21 Montana Deer Hunting Good Chance of Doe Estimation by Cluster variable Enthusiast Meat Genrl.-Meat Trophy Constant 3.3492 .4166 3.4127 1.9352 (T-Stats) (8.72) (.25) (7.11) (5.08) LBIDTRIP -.8643 -.9638 -.9301 -.5629 (-11.64) (-13.47) (-8.85) (-8.69) LINCOME — .3137 (1.94) — — LTRIPS -.3876 -.2354 -- -.3018 (-2.86) (-1.86) (-2.26) LDRSEEN ~ ~ — ~ LHUNTER ~ — — ~ LYRSHNT PURPOSE -.3349 (-1.66; DRKILL CLUB LAGE Sample Size 575 747 301 521 48 Table 22 Montana Deer Hunting Chance of Extra Deer Estimation by Cluster Variable Enthusiast Meat Genrl. -Meat Trophy Constant (T-Stats) LBIDTRIP LINCOME LTRIPS 4.7536 (7.96) -1.0593 (-12.29) -.3921 (-2.89) .9167 (.54) -.9874 (-13 .53) .4598 (2.81) 4.514 (7.47) -1.0897 (-8.99) (• 1.4406 -.75) (■ .8820 -11.10) .5281 (2.93) ( .4803 -3.37) LDRSEEN . 1640 (1.84) LHUNTER LYRSHNT PURPOSE DRKILL -.4795 (-2.16) .3700 (3.05) CLUB LAGE .3221 — (2.49) -.5645 (-1.93) Sample Size 576 740 302 517 49 Table 2 3 Montana Deer Hunting Net Economic Trip Values by Cluster CURRENT TRIP Method Enthusiast Meat Genrl. -Meat Trophy MEAN-LOGIT $ 297.44 181.92 315.08 MEDIAN $ 68.75 48.76 83.89 470.70 145.32 DOUBLE CHANCE OF MATURE BUCK Method Enthusiast Meat Genrl. -Meat MEAN-LOGIT $ 287.41 138.17 229.63 MEDIAN $ 80.80 37.67 48.75 Trophy 441.43 193.02 GOOD CHANCE OF DOE OR SMALL BUCK Method Enthusiast Meat Genrl. -Meat Trophy MEAN-LOGIT $ 163.65 120.42 150.52 211.86 MEDIAN $ 30.97 27.96 33.13 16.02 CHANCE OF AN EXTRA DEER Method Enthusiast MEAN-LOGIT $ 211.75 MEDIAN $ 61.32 Meat Genrl. -Meat Trophy 127.94 183.24 298.87 31.59 60.07 80.15 50 CHAPTER VII CONCLUSIONS The basic conclusion of this report is that there are significant recreation values associated with deer hunting in Montana. Specific major findings are as follows: - 5000 questionnaires were mailed to resident and nonresident holders of deer hunting tags with an overall response rate of 66.5 percent - of the 2950 returned questionnaires 2395 were from residents and 555 were from nonresidents - of the 2950 returned questionnaires 2786 hunters hunted on their own and 164 hunters hired guides - average expenditures per trip were $112.64 for residents, $1006.12 for nonresidents, $1591.95 for guided hunters and $217.47 for nonguided hunters - average expenditures per day were $25.08 for residents, $146.23 for nonresidents, $242.67 for guided hunters and $45.21 for nonguided hunters - the mean net economic value of a Montana deer hunting trip is $301.51 - the mean net economic value of a Montana deer hunting day is $61.40 - per trip net economic values varied widely between hunter subgroups with values of $208.74 for residents, $705.85 for nonresidents, $799.99 for guided hunters and $269.05 for nonguided hunters - hunters consistently ranked alternative hunting conditions with the chance for a large buck valued highest, the chance for an extra deer valued slightly lower and a good chance for a doe or small buck valued lowest - current trip values were not statistically different for the seven DFWP administrative regions - when hunters were clustered according to their motivations for hunting they showed significantly different net economic values for their deer hunting trips 51 REFERENCES Allen, S. (1987) Angler Preference Report. Helena: Montana Department of Fish, Wildlife and Parks. Allen, S. (1988) Results of the Elk Hunter Preference Study. Montana Department of Fish Wildlife and Parks. Bozeman, MT. Amemiya, T. (1981). Qualitative Response Models: A Survey. Journal of Economic Literature, 19, 1483 - 1536. Bishop, R.C. & Boyle, K. (1985). The Economic Value of Illinois Beach State Nature Preserve. Final Report to Illinois Department of Conservation, Madison, WI . Bishop, R.C. & Heberlein, T.A. (1985) The Contingent Valuation Method . Paper presented at the National Workshop on Non- Market Valuation Methods and Their Use in Environmental Planning, University of Canterbury, Christchurch, New Zealand, Dec. 2-5. Bishop, R.C, T.A. Heberlein and M.J. Kealy (1983). "Contingent Valuation of Environmental Assets: Comparisons With a Simulated Market," Natural Resources Journal 23:619-633. Bishop, R.C, Heberlein, T.A., Welsh, M.P., & Baumgartner, R.M. (1984). Does Contingent Valuation Work? Results of the Sandhill Experiment . Paper presented at joint meeting of the Association of Environmental and Resource Economists and the American Agricultural Economics Association and the Northeast Agricultural Economics Council, Cornell University, August 5-8. Boyle, K.J. & Bishop, R.C. (1984). A Comparison of Contingent Valuation Techniques. Department of Agricultural Economics Staff Paper 222, University of Wisconsin-Madison. Boyle, K.J., R.C Bishop, and M.P. Welsh (1985). "Starting Point Bias in Contingent Valuation Bidding Games," Land Economics 61: 188-94. Brooks, R. (1988). The Net Economic Value of Deer Hunting in Montana. Montana Department of Fish, Wildlife and Parks. Bozeman, MT. Bureau of Land Management. Final Rangeland Improvement Policy. Instruction Memorandum 83-27. October 15, 1982. Washington DC Cummings, Ronald, David Brookshire, William Schultze. 1986. Valuing Environmental Goods: An Assessment of the Contingent Valuation Method. Rowmand and Allanheld, NJ. Dillman, Donald. 1978. Mail and Telephone Surveys. John Wiley, New York, NY. 52 Duffield, J.W. (1984). Travel Cost and Contingent Valuation: A Comparative Analysis. Advances in Applied Microeconomics, Vol. 3, JAI Press. Duffield, J.W. (1988). The Net Economic Value of Elk Hunting in Montana. Montana Department of Fish Wildlife and Parks. Bozeman, MT. Duffield, J.W., R.Brooks and J.B.Loomis (1987). The Net Economic Value of Cold Water Fishing in Montana: A Regional Travel Cost Model. Helena: Montana Department of Fish, Wildlife and Parks. Duffield, J.W. and D. Patterson (1990) . Inference and Optimal Design for a Welfare Measure in Logistic Contingent Valuation. Forthcoming, Land Economics. Dwyer, J., J. Kelly and M. Bowes. (1977). Improved Procedures for Valuation of the Contribution of Recreation to National Economic Development. Research Report 77-128. Water Resources Center. University of Illinois at Urbana-Champaign. Hanemann, W.M. (1984). Welfare evaluations in contingent valuation experiments with discrete responses. American Journal of Acfricultural Economics. 66, 332-341. Just, R.E., D.L. Hueth and A. Schmitz (1982). Applied Welfare Economics and Public Policy. Englewood Cliffs, Prentice Hall, Inc. Loomis, J., J. Cooper and S. Allen. (1988). The Montana Elk Hunting Experience: A Contingent Valuation Assessment of Economic Benefits to Hunters. Montana Department of Fish, Wildlife and Parks. Bozeman, MT. Loomis, J., M. Creel and J. Cooper. (1989). Economic Benefits of Deer in California: Hunting and Viewing Values. Institute of Ecology Report #32, University of California, Davis, CA. Mitchell, R.C. & Carson, R.T. (1981) . An Experiment in Determining Willingness to Pay for National Water Quality Improvements. Report prepared for U.S. Environmental Protection Agency, Washington, D.C. Sassone, P. and W. Schaffer. (1978). Cost Benefit Analysis: A Handbook. Academic Press, NY. Seller, C. , J.R. Stoll and J. Chavas (1986). "Specification of the Logit Model: The Case of Valuation of Nonmarket Goods," Journal of Environmental Economics and Management 13:382-390. 53 U.S. Department of Interior (1986). 1986 Natural Resource Damage Assessments: Final Rule. 43 CFR Part 11, Federal Register Vol 58, No. 148, August 1. U.S. Water Resources Council (1983). Economic and Environmental Principles for Water and Related Land Resources Implementation Studies. Washington, D.C.: U.S. Government Printing Office. Welsh, M.P. (1986). "Exploring the Accuracy of the Contingent Valuation Method: Comparisons with Simulated Markets," Unpublished Ph.D. Thesis, Department of Agricultural Economics, University of Wisconsin-Madison. 54 APPENDIX A: SURVEY INSTRUMENT 55 •^ r Q- o '■Z -B O B (DC .?■ (/> y- 3 Jt: O Q. 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QJ dJ -^ C tf) -li: ~ O ♦- — .= _ U) 2 t- z 2 O 3 sg y (D >. z =5 — U) (D IT C a ~~ -C D) 5 - tfj *^ c 3 w o > 8 = >■ o O m CO £ )r the 1 wher Does Q. o >. o i; o . 9 = ; S O (E o Q O z > ^^ S tn Q< z z => o = 1 ^^ _l ~ _J o 5:s (/) m Z uj 25 t- o CO 05 LU DO oz -! < <° -I w 55 b APPENDIX B: ESTIMATED BIVARIATE MODELS 62 Table B-1 Montana Deer Hunting Estimated Bivariate Models Current Trip Question Model Constant Log (BID) N Entire Sample Montana Residents Nonresidents Guided Hunters Nonguided Hunters 3.6007 3.7218 4.8694 5.9726 3.6281 -.8393 -.9413 -.8340 -.9654 -.8691 2845 2306 539 164 2681 Table B-2 Montana Deer Hunting Estimated Bivariate Models Double Chance of Buck Question Model Constant Log (BID) N Entire Sample Montana Residents Nonresidents Guided Hunters Nonguided Hunters 3.8440 3.7436 5.8579 8.0949 3.8264 -.9113 -.9518 -1.082 -1.363 -.9317 2842 2305 537 162 2680 63 Table B-3 Montana Deer Hunting Estimated Bivariate Models Good Chance of Doe Question Model Constant Log (BID) N Entire Sample 2.6928 Montana Residents 2.8881 Nonresidents 2.2692 Guided Hunters 1.1705 Nonguided Hunters 2.8529 -.8343 -.9159 -.6249 -.3848 -.8821 2833 2300 533 159 2674 Table B-4 Montana Deer Hunting Estimated Bivariate Models Chance of Extra Deer Question Model Constant Log (BID) N Entire Sample 3.6965 Montana Residents 3.5815 Nonresidents 5.0311 Guided Hunters 4.2718 Nonguided Hunters 3.7353 -.9494 -.9914 -.9989 -.7846 -.9811 2810 2283 527 158 2652 64 Table B-5 Montana Deer Hunting Estimated Bivariate Models by DFWP Region Question Region Constant Log(BID) N 4.1367 -.9616 398 3.1894 -.7858 402 3.2487 -.7565 555 3.8784 -.8913 578 3.5708 -.8749 284 4.6196 -1.018 254 3.2246 -.7229 277 4.0176 -.9750 397 3.7862 -.9397 405 3.5068 -.8425 554 4.3255 -1.038 579 3.4922 -.8314 284 4.0181 -.8939 248 4.5389 -.9771 280 2.3179 -.7739 393 2.6712 -.8637 408 2.9427 -.8566 546 2.9932 -.8896 575 2.1143 -.7405 286 3.2964 -.9291 248 2.4954 -.8215 280 3.6616 -.9523 389 3.2505 -.9361 405 3.1222 -.8205 540 3.9715 -.9929 574 4.0298 -1.086 283 4.4245 -1.047 246 4.3207 -.9899 278 Current Trip Large Buck Doe/Small Buck Extra Deer 65 Table B-6 Montana Deer Hunting Estimated Bivariate Models Hunter Clusters Cluster Question Constant Log (BID) Generalist-Enthusiast Current Trip 3, .4834 -.8234 645 Large Buck 4, .0639 -.9253 644 Doe/Small Buck 2, .9964 -.8728 632 Extra Deer 4. .1713 -1.013 633 Meat Hunter Current Trip 3. .8929 -1.002 829 Large Buck 3, .8237 -1.054 833 Doe/Small Buck 3. .3228 -.9976 829 Extra Deer 3. .5106 -1.017 822 Generalist-Meat Hunter Current Trip 3. .8500 -.8713 346 Large Buck 3. .3111 -.8519 346 Doe/Small Buck 3. .3032 -.9536 346 Extra Deer 4. .5654 -1.115 346 Trophy Hunter Current Trip 3, .9568 -.7947 562 Large Buck 5, .7317 -1.089 562 Doe/Small Buck 1, .6588 -.5980 560 Extra Deer 3. .9026 -.8902 554 66