I. INTRODUCTION

Outdoor recreation economics has for decades emphasized recreation benefit estimation. This focus has led to the creation of a number of non-market valuation methodologies and a considerable literature devoted to their refinements. The market for this sort of analysis, outside of the economics profession itself, has been small. The reason for this is that the usefulness of this work seems largely confined to two types of situations; one where recreational valuation can help policy makers choose among alternative projects and the other within the context of evaluation completed projects.

Over the years there have been recommendations that the potential expand its analysis of outdoor recreation to include studies of resource allocation (Gum and Martin 1975), research on policy and management-related inputs (Batie and Shabman 1979), and more generally, analyses that are more consistent with models of recreational resource management as opposed to resource valuation (Matulich, Workman, and Grenville 1987). These suggestions are based on the observation that many resource managers are operating in a vacuum and that the potential market for management-related analysis is large. One area in which economists could be helpful is in the analysis of user regulations, particularly those designed to address congestion problems.

Deer Hunting With Rifle From The Local FFL Holder

The market increase in the demand for outdoor recreation has caused congestion problems that have had negative impacts on both the quality of the outdoor experience and the physical environment itself. From a management perspective these problems did not exist or were considered much less important thirty years ago. One solution to these problems is user restrictions. In this regard it is relatively easy to design rules that alleviate congestion or preserve a population of wildlife. The more difficult task is choosing the set of regulations that both controls the congestion problem and at the same time optimally allocates the recreational use of the resource. Markets that allocate by willingness to pay are not usable or even desirable distribution mechanisms for allocating publicly managed goods. Were that not the case, the management problem would reduce to a price-setting decision. Instead, managers often design a set of user restrictions that in theory solves the congestion problem. They then present the regulatory plan in public hearings. If there is no public outcry the regulations are put into place. Over time the managers try to evaluate the effect the regulations have on resource preservation and congestion.

More careful studies of the regulation of outdoor recreation would reduce the costs of the regulatory process both monetarily and politically. Managers would have better information on both the effectiveness of regulations in reducing congestion problems and the receptiveness of user groups to those regulations. This paper presents one approach for evaluating the demand for regulation in the context of the management of big game hunting. Though the empirical analysis focuses on regulations on big game hunting for deer and elk in Washington State, the model and empirical techniques may be applicable to other jurisdictions and recreational activities. In addition, the paper provides a detailed description of the structure of the random drawing distribution systems that have become common in the West for allocating recreational user privileges.

II. RANDOM DRAWINGS AS DISTRIBUTIONAL MECHANISMS

Game departments exist in all fifty states for the purpose of concurrently managing wildlife populations and regulating recreational hunting activity. Typically this task takes the form of a constrained maximization problem whereby agencies are instructed to maximize recreational opportunity subject to maintaining certain levels of wildlife populations.(1) Because most wildlife-related recreation is hunting, the management of the recreation is, in a sense, a harvesting problem.

In some states, species such as the grizzly bear and mountain caribou have zero harvest levels because the desired population is much greater than the actual population.(2) For other species such as blacktail jack rabbit and coyote, populations are either at or above the desired level and hunting activity is not regulated. People can hunt them as they please.(3) Deer, elk, black bear, and waterfowl are species for which the desired harvest level is positive but must be constrained through regulation. The Task for game managers in these cases is to devise regulations which allow for adequate harvest and also “maximize” recreational opportunity. For example, if the desired deer harvest is 100 animals, a three-month season restricted to bow and arrow hunting may be as effective as either a two-day season where hunters can use modern firearms or a four-week season in which hunters maya only use muzzle loading (primitive) firearms. Numerous combinations of these might also meet the harvest objective but the best choice of regulations may not be clear because there is little or no information on the demand for each of the different activities.

One management approach employed when congestion is a problem or when open access to hunting grounds would result in overkill is to limit access to a fixed number of permit holders and to distribute the permits by random lottery. This allocation scheme is used in a number of western states to distribute permits to hunt non-antlered deer. Those wishing to hunt submit applications for entry into a lottery from which hunters are randomly chosen. The number of permits is based on the game department’s harvest goal and estimated hunter success.

Random drawings of this type are used in fifteen western states and Canadian provinces to distribute access rights for big game hunting for moose, deer, elk, bighorn sheep, mountain goats, and musk ox. In the eastern United States random drawings are used to distribute the rights to blinds for waterfowl hunting on public lands.(4) A major reason these lotteries are used is that individuals’ abilities to pay do not become a factor in the distribution process.(5)

The lotteries used to allocate big game hunting permits have a number of common characteristics. The permits are generally for specific geographical areas within which holders must confine their hunting. In addition, restrictions on individual permits usually specify the types of weapons hunters may use, the period of time for which the permit is valid, and the sub-species and sex of the animal. In the case of antlered and horned game, hunters are often allowed to hunt only for animals with particular size horns or antlers. While there usually are a large number of lottery-drawn permit hunts from which to choose, hunters are allowed to participate in only one per species.

The study of participation in these permit lotteries can provide valuable information for game managers. Perhaps most important is that game managers believe relative demands for different regulations exhibited in the permit hunts closely parallel relative demands for the same regulations during the general hunting seasons. This allow managers to use information about permit regulations to set general regulations and thus be more answerable to hunter preferences. Other reasons for wanting information on demand include a preference for regulatory simplification and the desire to measure the cost effectiveness of regulations, especially those that are hard to enforce.

III. THE LOTTERY DISTRIBUTION MODEL

The rules of big game permit drawings dictate certain attributes of the model: (1) winners are chosen randomly; (2) the supply of permits is fixed before each drawing; (3) entry is limited to one per person; (4) entry into one drawing precludes entry into any other; (5) permits are not transferable. It is furthermore assumed that potential drawing participants are risk-neutral wealth maximizer who want to maximize the expected value of lottery participation. They are fully informed regarding the supply and characteristics or permits, regulations governing use, and the number of participants in each drawing.(6)

Let [V.sub.j] (Y, P, H, [q.sub.j]) be the amount of money an individual would be willing to pay for permit j were it available with certainty. The [q.sub.j]’s are the characteristics of the jth permit. These include the recreational benefits associated with the permit and the various regulations governing use. Y, P, and H are income, prices, and household characteristics, respectively. Let [S.sub.j] and [N.sub.j] be the supply of permits and the number of entrants into drawing j.(7) [S.sub.j]/[N.sub.j] is the probability of winning permit j. For ease of notation let it be equal to [Mathematical Expression Omitted]. Lastly, let [P.sub.L] be a non-refundable, drawing entry fee. [Mathematical Expression Omitted] is the expected value of entering lottery j and drawing a permit. [Mathematical Expression Omitted] is the expected value of entering but not being drawn. The expected value of entering the jth permit lottery, E([L.sub j]), is simply the sum of the expected values of its outcomes or [1] [Mathematical Expression Omitted]

A risk-neutral wealth maximizer is willing to participate in any lottery only if the expected value of the outcome is greater than or equal to zero or when [2] [Mathematical Expression omitted]

The rules allow participation in only one drawing and hence the individual will enter the drawing with the highest expected value. We can describe the individual’s decision process as a set of binary indices, [d.sub.1], . . . [d.sub.n], where [d.sub.j] equals 1 if the jth drawing is chosen. Otherwise [d.sub.j] equals 0. For the wealth-maximizing individual the choice is described by [3] [Mathematical Expression Omitted]

These [d.sub.j]’s are the individual demand curves for permits given lottery rules and permit parameters. Though changes in the price of entry, [P.sub.L], will not cause an individual to switch from one lottery to another, a change in the entry price can effect the decision to participate in the lottery system at all. This is because the entry price is the same in all drawings and though a different price does not effect relative rankings of their expected values, it does not effect the nominal values. For example, an increase in [P.sub.L] could cause all lotteries to have an expected value less than zero, hence no participation.

Changes in the recreational characteristics that give value to a permit might cause an individual to switch to another lottery in the system or not participate at all. For instance, an increase in the success rates of hunters holding permit j would increase its value. The increase in value increases the likelihood that a hunter would choose the j permit’s lottery. Likewise, a decrease in hunter success rates would decrease the likelihood of participation. Changes in other permit characteristics, including changes in hunter regulations, would have similar effects on permit value and lottery choice.

Deer Hunting

The sum of the individual demands gives the aggregate demand for each type of permit. This can be represented as [4] [Mathematical Expression omitted] where [N.sup.*] is the total population of potential lottery participants and [d.sub.jv] is individual v’s demand for participation in the lottery for permit j. The set of [D.sub.j] are equilibrium levels of participation for the population [N .sup .*]. Individuals have behaved in a way that maximizes wealth and no one can increase his or her wealth by not participating or by switching lotteries.

Certain standard characteristics of demand equations should be observable regarding these functions. Increases in the price of entry should decrease participation in the j lotteries. Growth in the population or in the population’s incomes should increase participation.

Changes in supply of a particular permit and changes in regulations governing use also have predictable effects on demand. An increase (decrease) in the supply of any particular permit, [S.sub.j], will cause an increase (decrease) in the demand, [D.sub.j], for that permit. The increase is bounded however, because the percentage increase in [D.sub.j] will be less than or equal to the percentage increase in [S.sub.j]. The reason for this is most easily seen if we look at two extreme possibilities. First, a change in [S.sub.j] will alter the probability of winning a permit and thus the expected value of being in a lottery. If an increase in the supply is not sufficient to cause anyone in the population to alter his/her wealth-maximizing decision, [Delta][D.sub.j]/[Delta]S will equal zero, non-participants in the lottery will remain so, and participants in other lotteries will not switch. There will be an increase in wealth for participants in the lottery with the enlarged supply.

Another possibility is that the increase in the supply of a particular permit and the resulting increase in the expected value of entering would cause participation in that lottery to rise. The increase in participation would never be proportionally greater than the increase in the permits. This is because a proportionately greater increase would imply that the expected value of winning that permit would decrease, and lower expected wealth was preferred by some members of the population. Mathematically then, [5] [Mathematical Expression Omitted]

Changes in the aggregate demand for permits can also be caused by changes in the characteristics of a permit. This is because a change in a permit characteristic can alter individuals’ valuations of the permit and thus their expected values of that permit’s lottery. It follows that the likelihood that individuals will enter that lottery also changes. Additions of characteristics that are perceived as positive recreational benefits will increase aggregate demand. Decreases in positive recreational benefits will have a negative effect.

A special case of this is caused by the adoption of permit-use restrictions. These limit the activity of holders of one type of permit relative to the activity allowed by other permits. When adopted, these regulations have either a zero or negative effect on demand. To see this, assume all permits allow holders to choose among ten different activities. A restriction is imposed on one permit but not on the others. That restriction allows permit holders to choose between only two activities. The other eight are no longer allowed. If all of the participants chose one of these two activities, even when the other eight were allowed, the imposition of the regulatory restriction on those eight activities would have no effect on the expected value of participation. The regulation would be superfluous and non-binding. The demand for that permit would not change. If, on the other hand, some participants favored one of the eight activities made unavailable, they would experience a decrease in expected value and this would lower demand.

Where [q.sub.j] is the adoption of a regulation designed to restrict

activity, the demand effect of its adoption can be described as [Mathematical Expression Omitted]

IV. THE WASHINGTON STATE PERMIT SYSTEM

Permit-only hunts for deer and elk were established in Washington State in the mid-1960s to harvest the surplus female deer and elk that were not harvested during the buck deer and bull elk general seasons. A permit-by-drawing system was instituted because demand for permits was higher than the game department could supply without an overkill of female animals. Drawings were set up for different geographical areas called game management units, and the number of permits available in each depended on the harvest goal for that area and the anticipated hunter success. By winning, the permit holder gained the right to hunt animals of either sex in the designated area while retaining the right to hunt male animals during the general elk season.(8)

In the 1970s the game department began using permit hunts to spread out hunting pressure, control congestion, and provide special types of hunts for hunters wanting to use primitive weapons or to hunt for trophy animals. At the same time some permit hunts were made “antler less-only” in order to assure an adequate harvest of the female animals.

Since their inception there have been approximately 36 deer and 33 elk permit drawings per year. In each of those years there have been about 25,000 applications for 4,000 deer permits and 35,000 applications for 5,000 elk permits. Demand for these permits is high because of the increased probability of success if the hunter can shoot animals of either sex. Although there is a high variance across game units, average success during the general deer and elk seasons is 14 and 8 percent, respectively. Success for elk and deer hunters with lottery distributed permits has averaged 45 percent. Since 1970 the probability of being awarded a permit in any single drawing has ranged from 0.05 to one. Information on permit lotteries is well distributed. Data on drawing participation, regulations, permit holder success, and permit area characteristics are published yearly by the Washington Department of Game. In addition, a private map company produces and sells maps that contain permit drawing statistics, success data and information on wildlife populations, public access, and regional weather for the last five years.(9)

Demand for permits is a function of the population household characteristics and incomes, prices, and the supply and characteristics of permits. Complete specification of a model to describe this demand presents a formidable data specification and collection task. It would require detailed cross-sectional and time series data on population characteristics, incomes, prices of transportation, and alternative recreational activities. It also would require detailed specification of the permit and area characteristics, the latter being numerous. For example, eastern Washington elk hunting areas are open, dry, and rugged mountainous country with deep snow in some years. They are farther from major population centers than western Washington areas and have Rocky Mountain elk rather than western Washington’s Roosevelt elk. Western game units require hunting in dense, brushy, often rain-forest-like terrain. Units all over the state contain various amounts of public land which along with the number and quality of roads affect accessibility. Hunting experiences across units are extremely varied.

Specifying and collecting the data necessary to describe game units and population characteristics were not feasible. However, because so many of the characteristics particular to a permit are specific to a game unit area, and because many population characteristics are time specific, a covariance model was usable as the measurement device. Two sets of these fixed-effect variables were used in this study. Because many characteristics differ across areas, but are fixed over time, a dummy variable was used for each area in order to pick up differences in permit demand due to the game unit variability. The type of information each of the area variables would incorporate includes characteristics such as the area’s terrain, species of elk and deer, and proximity to human population centers. Time-related dummy variables were included to encompass such factors as population growth, changing prices, and variations in hunter incomes and tastes that may have occurred over the study period.(10)

Data were collected on 368 deer- and 242 elk-permit drawings conducted in Washington State from 1973 through 1982.(11) For each drawing, information was recorded on the number of applicants, the number (supply) of permits available, the previous year’s percentage of hunters holding permits who were successful in bagging an animal,(12) and the various special regulations that governed permit use for that permit area in that year. The regulations for the deer-permit lotteries were antler less animal, whitetail deer species, and primitive weapon (muzzle loader) hunting. For the elk-permit drawings the regulations included, in addition to the antlers and primitive weapon hunts, a trophy-only restriction (minimum three antler points per side) and a late-season regulation. The trophy hunts were in response to requests for high-quality hunts. The late-season regulation specified that a hunter who applied for one of these permit hunts could no longer hunt the first three to five days of the general season whether drawn for a permit or not. This regulation was designed to decrease congestion at the beginning of the hunting season. A variable was also included to identify the elk-permit hunts affected by the volcanic eruption of Mount St. Helens. No deer-permit hunts were affected.

Tables 1 and 2 show the form of the equations and the variable definitions for the deer- and the elk-permit systems separately.(13) Note that [APPS.sub.i], the number of applicants into lottery j, is the empirical equivalent of the theoretical [D.sub.j] in the previous section. Likewise, [PERMS.sub.j], the supply of permits available in lottery j, is the empirical equivalent of the theoretical [S.sub.j]. It is the natural logarithms of these variables (LN(APPS), LN(PERMS)) that are used for the estimation procedures.

The coefficient on the natural logarithm of the supply of permits variable (LN (PERMS)) should be greater than zero but less than one. The coefficients on the regulatory restrictions (MUZZLE, AO, TROPHY, TAG1 and WTAIL) should be negative or zero. It is further anticipated that the coefficient on the success variable (SUCC) will be positive since success is generally considered a positive attribute by hunters.

Tables 3 and 4 show the results of ordinary least square estimation for the elk- and deer-permit equations. The estimated coefficients are all of the predicted sign and in the case of the permit supply variable, LN(PERMS), of the predicted magnitude in both the deer and the elk equations. In both cases the antler less restriction and the hunter success variable have coefficients that are not significantly different from zero. A surprising result is that all of the matching coefficients (the ones on LN(PERMS), AO, MUZZLE) in each of the two separate equations are not significantly different from each other. This is true even though the equations are generated from two different data sets and the equations are different in that the elk equation has more variables. Table 5 shows the effect of each regulation on the number of applications into permit lottery drawings when the effect is calculated at the mean of applications for each of the samples.

The estimate on hunter success is positive, as anticipated, but insignificant. This runs counter to the expectation that hunter success has a large positive effect on the expected value of a hunt. One explanation for the lack of significance is that the effect the differences in hunter success might have on participation has been captured in the area dummy variables. Any variability through the years in success within individual areas may simply be too small to capture empirically.

The negative coefficient on the VOLCANO variable is consistent with the presumption that the apparent devastation of elk habitat and the difficulty in hunting caused by the Mount St. Helens eruption might cause a decrease in demand for permits.(14)

V. POLICY IMPLICATIONS

Altering hunting regulations based solely on their impact on lottery participation cannot systematically lead to efficiency gains. A change in a regulation could cause increases in lottery applications while increasing or decreasing the net benefits of the hunt. From the standpoint of Pareto optimality the analysis here provides little insight. In practice, though, Pareto optimality is of little concern to game managers. Their interests lie less in the net economic benefit of the hunts than in the number of constituents who feel affected by changes in regulations. Given that, permit lottery analyses can provide valuable information.

The original purpose of instituting the permit-only hunts was to cull and harvest surplus female animals. Permit hunts were designated either-sex hunts to allow hunters to harvest male or female animals. Because it was more difficult to predict how many of the permit hunters actually would take males rather than females, the either-sex designation has been less desirable from a herd management perspective. It has always been presumed that it gave hunters more options, and was therefore in higher demand, than an antler less-only restriction. The results in this study show that in relative terms the regulation that limits hunters to bagging only antler less animals has little effect on permit demand.

This finding runs counter to information from public hearings. At these, hunting-club representatives often argue that hunters do not want antlers-only hunts. Though hunting-club membership is a very small proportion of all hunters in the state, the clubs’ input is well organized and often dominates the public record. The discrepancy between the public-hearing testimony and the results shown here points out the problem with the information collected in public hearings. It also shows how the analysis presented here can help to better inform policy makers.

Another important finding concerns the trophy and primitive weapon hunts. Each of these regulations causes a significant decrease in demand. The trophy-hunting rule for elk hunts caused a decrease of 55 percent. The primitive-weapon regulations decreased demand by 70 percent for both elk and deer hunts. This information gives some support to arguments that these hunts are a low priority to hunters and should be limited.(15)

The small demand for trophy-only hunting has some very significant implications for future herd management. In response to requests in public hearings, the game department is starting to restrict more and more areas to trophy-only hunting. This policy is in response to the hunting clubs’ requests for more trophy hunts. The findings presented here suggest that this policy is not attractive to a large number of hunters. A more careful review of the policy, and further study of the issue, may be in order. Had the analyses shown a very high demand for these trophy hunts, support could be given for policies that would increase the number of trophy animals in a herd. Such policies, though, are at the expense of other types of hunting.

The late-season hunting restriction translates into a 25 percent reduction of hunting pressure at the beginning of the general elk season. This corresponds well with the desired goal of a 30 percent reduction in hunting pressure that the department originally hoped for with the restriction.(16)

Though late-season hunting to control congestion and buck deer trophy hunting are not now part of the Washington deer hunt regime, both have been suggested as future regulations. The nearly identical effects of the antler less-only and primitive-weapon restrictions across deer and elk hunting may make it possible to predict similar effects if the late-season and trophy hunts were added to the deer-permits system. If so, managers can anticipate relatively small demand for deer trophy hunts and an effective congestion reducer from a late-season deer regulation. An extension of this rationale would suggest that if the game department wished to try other regulations it would be possible to introduce them in one of the hunting activities, that is elk or deer, and after measuring the effect, anticipate a similar outcome in the other.

A broader application of these results would be to apply them to regulations for the general hunting seasons. Again, if the effects of regulation on demand in one set of permit hunts can be applied to the general season hunts, managers have a valuable laboratory in the permit system. Some support for this approach comes from some recent hunting rule changes for deer. General season hunts in 1986 and 1987 that restricted all hunters to hunting only trophy buck deer in certain game units resulted in an estimated 50 percent reduction in hunting pressure in those areas. This is almost identical to the decrease measured using elk-permit data and shown in Table 3. (1)For example, in Washington this is a specific charge. The Revised Code of Washington, (RCW), 1981, 77.12,010) reads that the game department is in charge of the “preservation, protection and perpetuation of wildlife,” and “the setting of hunting and fishing regulations which maximize public recreational opportunity without impairing the supply of wildlife.” (2)This is being overly general. Many states have neither the desire nor the capability of sustaining any population of such animals. In other cases certain animals are protected by state or federal law and hunting is not allowed regardless of the size of the population. (3)In the past, certain animal species, most notably the wolf, have been subject to bounty hunting. This consisted of using monetary rewards to increase harvest when populations were felt to be too high. In the west bounty hunters are still used by time be companies to control black bear and beaver. (4)In addition to their use in game management, random drawings are also used to control congestion in non-hunting activities. For example, they are used to allocate permits to float the Salmon River in Idaho and to distribute daily permits to climb Mount St. Helens in Washington. (5)Many of these drawings require a small fee to cover costs. (6)The rationale for these rules is policy based. The fixed supply of permits is based on desired harvest. Lack of transferability and the limit of one entry into the system per person are designed to protect against having wealth become a factor in the selection process. (7)We assume that [N.sub.j] is sufficiently large so that [S.sub.j]/[N.sub.j], the probability of winning permit j, is exogenous to the individual. (8)Some of these rules have the changed since 1985. (9)See of instance, “RECON Charts for 1985: Washington State Elk Hunters,” Enerad Inc., Bellevue, Washington. (10)Were there a significant interaction between the two sets of dummy variables, an error components model would be a natural alternative to the covariance model. Because major characteristics of the game units have changed little or not at all over time it is assumed no such interaction occurs. (11)The 368 deer drawings used in the study represent all of the deer-permit drawings in the state from 1973 through 1982. There were a total of 336 elk-permit drawings conducted during the same period. For 94 of these the unit definition data was incomplete. For instance, units with different geographical boundaries would have the same identifying unit number in different years. Because the problems proved irreconcilable, these were not included in the analysis. All of these units were on the Olympic Peninsula where less than 15 percent of the state’s elk hunters hunt. (12)A five-year moving average of success was also calculated but no difference in results was found. Those results are not included. (13)Because it was conceivable that more restrictive forms of the model would be better estimators of demand, regressions were run on three other models. In the first it was assumed that neither the differences across time nor permit areas would shift demand and the YEAR and AREA dummy variables were omitted. In two alternative model forms, one of these variables was omitted while the other set was kept in the equation and asked to obtain their ffl license. . F tests were performed to compare intercept terms and based on these the model including both sets of dummy variables was chosen as more appropriate. (14)The elk herds are now thriving in the volcano area in spite of the moonscape environment in which they live. (15)In fact, the hunters who want to hunt with primitive weapons or for trophy animals get considerable benefit from these regulations. The profitability of being drawn for a few primitive-weapon elk hunts with

Demand for the Regulation of Recreation: The Case of Elk and Deer Hunting in Washington State

has been as high as one. This is considerably higher than others. (16)Washington State Department of Game, 1978. Big Game Report, Vol. 17.