The Recreational Economic Value of the Eastern Trinity Alps Wilderness

Steven C. Hackett
School of Business and Economics
Humboldt State University
Arcata, CA 95521
19 January 2000

Running Head: Recreational Value of the Trinity Alps

Keywords: Economic Benefits, Economic Valuation, Recreation, Travel Cost Method, Wilderness

I would like to acknowledge the assistance of Jim Holmes and Tom Hatcher, both of the Shasta-Trinity National Forest, in providing access to the wilderness permit database from the Weaverville Ranger Station. I would also like to express my gratitude for the valuable insights and helpful comments provided by John Loomis, Tom Lyon, and Dan Ihara.

The zonal travel cost method (TCM) is used to measure the recreational economic benefits from wilderness visitation in the eastern Trinity Alps of California. The zonal TCM involves aggregating visitation data by county zones of origin, and computing travel cost from the zone to the study area. Visitors are estimated to have spent a total of $566,058 in direct travel expenditures to access the wilderness experience in the eastern Trinity Alps. These visitors are estimated to have received a total of $219,028 in net benefits from their wilderness recreational experience, over and above the cost of traveling to the wilderness area, or $29.28 per individual visit. Based on the net benefits from recreation and the discount rate recommended by the U.S. Forest service, the wilderness resource is estimated to have a capital value of $5.48 million.

The wilderness experience cannot be completely reduced to a dollar value. From an economic point of view, however, wilderness areas contain a considerable stock of natural capital, and if the functional integrity of this natural capital can be maintained, then a flow of ecosystem services and recreation benefits can be sustained into the indefinite future. Those land management agencies that are charged with managing wilderness areas have sharply limited and sometimes politicized budgets, and so the resources necessary to perform these tasks may have a very high opportunity cost, both financially and politically. If some value-generating activity must be passed up in order to fund wilderness area maintenance and management, managers may eventually need to assess the benefits generated by the wilderness area. In this paper I investigate the recreational economic benefits associated with the wilderness experience. This paper does not attempt to determine the full economic value of the Trinity Alps wilderness. In particular, the analysis does not measure existence, option, or bequest values held by those who do not actually travel to visit the wilderness area. One should also keep in mind that economic benefits are only one facet of the value of the wilderness experience, many aspects of which are not amenable to economic measurement.

There are a number of techniques that have been developed by economists that can be used to assess the economic benefits generated by wilderness recreation. Two prominent methods are the contingent valuation method (CVM) and the travel cost method (TCM). In its contemporary form, the CVM uses survey research techniques to elicit individual responses to the hypothetical question of whether the respondent would be willing to pay a particular dollar amount in return for a well-defined environmental benefit. The CVM has the advantage of measuring both active use values from recreation as well as passive existence values, but the method involves costly survey research, and is controversial because it measures economic benefits based on hypothetical prices. Moreover, CVM responses often suffer from embedding bias, in which respondents behave as if they value protecting, say, 5,000 migrating ducks just as much as protecting 50,000 ducks or even 500,000 ducks (see Desvousges et al., 1993, and Diamond and Hausman, 1994). Embedding bias implies that the respondent’s choice behavior violates the axiom of local nonsatiation (more is better) which underlies the neoclassical economic model of consumer choice.

The TCM is based on the notion that the money and time that people spend traveling to an outdoor recreation area indicates the economic value of the recreational resource. For accessible introductions to the TCM see Loomis and Walsh (1997), Bockstael et al. (1991), Clawson and Knetsch (1966), and Clawson (1959). The TCM was first proposed by economist Harold Hotelling in a letter to the U.S. Park Service, in which he suggested that the full cost of visiting a park must necessarily include the cost of getting there (Hotelling, 1949). While the TCM only measures economic benefits from recreational visitors, and thus ignores existence values, the TCM draws on actual travel cost expenditures, rather than hypothetical responses. Researchers using the TCM must either assume that the study area was the sole purpose of the travel, or conduct their own survey and ask each individual to estimate the portion of their travel that is attributable to the study area. On the one hand remote wilderness areas are more likely to elicit single-purpose travel than, say, state parks along interstate highways, but on the other hand many visitors are likely to visit no more than once during the study period. The latter implies that individual visitation may not vary with travel cost, making it difficult to estimate recreational demand based on individual visitor data. The zonal method, which utilizes existing wilderness permit data and explains visitation from geographical zones of origin, is appropriate in such circumstances, and is employed here.

The study focuses on recreational visitation in the eastern portion of the Trinity Alps Wilderness in northwestern California. Geographically, the study area is bounded by the North Fork of the Trinity River and the Salmon River drainage to the west, the wilderness boundary on the south and east, and the Pacific Crest Trail on the north. One reason for this focus on the eastern portion of the wilderness area is the pattern of recreational use. The study area consists of steep mountainous terrain characterized by jagged granite peaks, forested valleys, and timberline lake basins, and is intensively used by backpackers, hikers, equestrians, and hunters. In contrast the western portion of the Trinity Alps wilderness is lower in elevation, consists of forested ridges and valleys mostly lacking in lakes, and consequently receives considerably less recreational visitation. Another reason, described in more detail below, is that electronically coded wilderness permits for 1999 were only available from the Weaverville ranger station, which primarily serves the eastern side of the wilderness area.

The primary data are comprised of individual wilderness permits that were filed at the computerized wilderness permit kiosk in the Weaverville ranger station during 1999. Nearly all visitation occurs in the period between Memorial Day in late May and Columbus Day in mid-October. A considerable portion of the wilderness area immediately to the west of the study area burned in a large wildfire (Big Bar Complex) during September and October of 1999. Smoke and ash from this fire limited outdoor activity in Humboldt and Trinity counties, both of which contribute a disproportionate number of visitors to the study area. Consequently it is likely that the fire caused wilderness visitation in the study area to be below normal levels. A number of fragmentary and obviously duplicate permits were deleted from this database, and Forest Service personnel removed the names and addresses from the permits to assure anonymity before providing them for analysis. As a result the primary data set used in this analysis consists of 1,518 individual wilderness permits filed by wilderness visitors. Each permit contains information on the size of the party covered by the wilderness permit and the place of origin of the person filling out the permit.

At the time of this study the Weaverville ranger station had the only electronic wilderness permit system for the study area. Paper permits are also filled out for visitation to the study area at the Big Bar and the Coffee Creek ranger stations. Unfortunately these permits have not been electronically coded to create a unified database for wilderness visitation in the study area. Tom Hatcher, the recreation officer for the Weaverville and Big Bar districts, estimated that the electronic database from the Weaverville ranger station accounts for 75 percent of all wilderness permits filled out by recreational users of the study area. Hatcher also estimates that 80 percent of all wilderness visitors to the study area complete a wilderness permit. Consequently the primary data used in this study is estimated to represent 60 percent (75*80) of all wilderness visitation to the study area during 1999.

The economic value of recreational use benefits was estimated using the zonal travel cost method, a standard method of benefits assessment with procedures and guidelines provided by the U.S. Water Resources Council (1983). The procedure aggregates individual visitation in the primary data set by county of origin listed on the wilderness permit. Since many people only visit the Trinity Alps once a year, making it difficult to estimate individual visitor demand curves using travel-cost prices, the zonal TCM explains the fraction of each county’s population that visits the study area as a function of travel cost. Thus each observation in the final data set is made up of information on per-capita visitation, income, and travel cost from a county zone of origin.

One of the assumptions of the travel cost method is that the visit occurs as a result of a single-destination trip, so that all of the travel cost borne by visitors from their point of origin to the study area can be attributed to the wilderness visit. Remote wilderness areas are more likely to meet this criterion than, say, state parks along busy highways. Nevertheless wilderness permits do not record whether or not the wilderness recreation was the sole purpose of the travel. Loomis and Walsh (1997) argue that one method of mitigating for multiple destination travel is to choose a geographical boundary for the recreational site that serves as the "market" for the recreational experience. People who travel from extraordinarily long distances are more likely to be on multi-destination vacation trips. A standard procedure in accordance with federal guidelines is to include all zones of origin that together account for approximately the nearest 95 percent of all visitors, assuming that the approximately 5 percent representing the most distant visitors are on multi-destination trips. These observations are excluded from the travel cost analysis, and their benefits are assumed to be equal to the average of those in the analysis. As applied here, this procedure resulted in 55 permits being excluded from the analysis, representing approximately 3.6 percent of the primary permit data. The final database included 69 observations, each representing total per-capita visitation, income, and travel cost data from a particular county zone of origin.

Several other assumptions are made in this zonal travel cost analysis. One of these assumptions is that characteristics of the population not quantified and included in the study are the same across the various zones of origin. The only demographic characteristic included in this study is per-capita personal income averaged by county zone. Another assumption employed in the zonal TCM is that wilderness visits are of equal duration. Since each observation in the final data set is a county zone of origin, it is not possible to include data on visit duration from individual permits. It is assumed that visitors travel by way of automobile, that all visitors listed on a given permit travel together, and that each have the same opportunity cost of an hour in transit. Finally, since wilderness permits only record the point of origin for the person filling out the permit, it is assumed that all individuals listed on a given permit travel from the county zone of origin indicated on the permit.

An individual's direct travel cost from their county of origin to the study area is the sum of their share of direct automobile transportation cost and an estimate of the value of their time spent in transit. According to the Transportation Energy Data Book the average variable cost per mile of operating an automobile in the U.S. is $0.1058 (Oak Ridge National Lab, 1999). It is assumed that each member of the party listed on a wilderness permit travels together in a single vehicle and equally share the transportation cost. As a result the transportation cost from the county zone of origin to the study area is $0.1058 times the round-trip mileage from the county seat of the county zone of origin, divided by the average number of visitors listed on the permit in the primary data set. Round-trip mileage was found by using the free travel route mapping service provided by the Excite web portal (maps.excite.com). The community of Dedrick, near the popular and centrally located Canyon Creek trailhead, was used as the common destination point in computing travel distance from the county seat of each county of origin to the study area.

The opportunity cost of a traveler's time in transit is valued at the California minimum wage of $5.75/hour. Loomis and Walsh (1997) observe that drivers appear to value their travel time at between one-quarter and one-half of the relevant hourly wage rate. The California minimum wage is used here because it is approximately one-half of the average hourly per-capita personal income in the county zones included in this study, and thus would appear to provide a reasonable estimate of the value of time in transit. As a result round-trip travel time from the county seat of the county zone of origin is multiplied by $5.75 to arrive at the opportunity cost of time in transit. The free travel route mapping service provided by the Excite web portal includes an estimate of time in transit. Travel cost to the study area is thus the sum of the transportation and time cost for the round-trip from the county seat of the county zone of origin.

The final data set of 69 observations is used to estimate a resource demand curve, as described in the section that follows. To estimate a resource demand curve using the zonal travel cost method one includes data on per-capita personal income and the price of one or more substitutes. The two recreational substitutes used in this study were Yosemite National Park (with Tuolumne Meadows, California, as the common destination point), and the Three Sisters Wilderness (with the town of Sisters, Oregon, as the common destination point). Like the Trinity Alps, these areas are at the core of large backcountry wilderness complexes and provide opportunities for high quality wilderness recreation. Moreover, together these areas bracket the study area and thus offer distinct substitutes for travelers from the north and the south. Thus each observation in the final data set contained information on per-capita county visitation, per-capita county personal income, travel cost to the Trinity Alps, travel cost to Yosemite, and travel cost to the Three Sisters Wilderness.

As outlined by the Water Resources Council (1983), the zonal TCM derives economic benefits using a two-stage process. First, regression analysis is used to estimate a demand function for the resource in question. Second, progressively higher travel costs to the study area are introduced to the estimated demand function to derive a set of forecasted visitation levels from each county zone of origin. These forecasted visitation levels are horizontally summed at each increment of additional travel cost, with the result being the final resource demand curve. The area under the resource demand curve represents the net economic benefits that flow annually to recreational visitors to the study area.

Accordingly, the statistical technique of ordinary least squares multiple regression analysis was used in the first stage of the analysis to estimate a linear demand function for recreational use of the eastern Trinity Alps. The dependent variable was the natural logarithm of per-capita county visitation rates. The independent variables included a constant term, per-capita income by county, the travel-cost price of visiting the study area by county, and the travel-cost price of visiting the two alternatives, Yosemite and the Three Sisters Wilderness, by county zone of origin.

The regression results are given in Table 1 below. Recall that the dependent variable is the natural log of per-capita county visitation rates to the eastern Trinity Alps Wilderness.

Table 1: Regression Results

^a Significant at the 1 percent level. ^b Significant at the 5 percent level.

The F-statistic for the regression was 29.13 (n = 69), indicating that one can easily reject the null hypothesis that all coefficients are zero. R² was 64.5 percent, and the adjusted R² was 62.3 percent, indicating that the model explains nearly two-thirds of the total variation in the data. In their survey of the TCM Loomis and Walsh (1997) observe that R² values exceeding 50 percent are considered acceptable in empirical demand estimation. The Durbin-Watson statistic was 2.05, indicating no significant autocorrelated disturbances, which we would expect with cross-sectional data such used here. The null hypothesis that the regression residuals are normally distributed can be maintained here at the usual significance levels (Anderson-Darling p-value is 0.275).

All coefficients are significant at the 5 percent level or better, with the exception of the coefficient for travel cost to the Three Sisters Wilderness, which is significant at the 11 percent level. The sign of the coefficient for travel cost to the eastern Trinity Alps is negative, as hypothesized in the zonal TCM, indicating that all else equal, counties with a higher travel-cost price of visitation to the study area tend to have a lower per-capita visitation rate. The signs of the coefficients for travel cost to the two substitute destinations are both positive, which is consistent with microeconomic principles. All else equal, counties that are far away from a substitute wilderness recreational experience, and which thus feature a higher travel-cost price of visiting the substitute, tend to have a higher per-capita visitation rate to the Trinity Alps. This is the principle of substitution at work. In a more familiar context the principle would suggest, for example, that if the price of Pepsi were to rise, consumption of Coke would rise. The positive coefficient for county per-capita income is consistent with the notion that wilderness recreation is a normal good, with rates of visitation increasing with per-capita county personal income.

Based on actual travel costs incurred by visitors to the eastern Trinity Alps, the estimated demand function forecasted 3,632 visits, while actual visitation from the 69 county zones of origin was 4,310. Thus the regression analysis forecasted 84.27 percent of actual visitation, an underestimate of 15.73 percent. Loomis and Walsh (1997) observe that as a rule of thumb, the estimated demand function is adequate for purposes of benefits assessment if the total of predicted visits based on actual travel costs incurred by visitors is within 20 percent of actual visitation. The regression model employed here satisfies this standard.

As indicated by the methodology for the zonal TCM, progressively higher travel costs to the Trinity Alps were then introduced in the second stage of the analysis in order to derive forecasted visitation levels from each county zone of origin. Once the regression equation was exponentiated to remove the natural logarithm, these forecasted visitation levels were then summed at each increment of added travel cost to derive the resource demand curve. The area under the resource demand curve represents the annual flow of net economic benefits to recreational visitors to the eastern Trinity Alps Wilderness.

The estimated resource demand curve is given in Figure 1 below:

The 4,473 individual visitors to the Trinity Alps Wilderness who are recorded on wilderness permits filed at the Weaverville ranger station in 1999 are estimated to have spent $339,635 in direct travel cost to access the wilderness experience, or an average of $75.93 per visitor. The statistical analysis estimates that these visitors received a total of $131,417 in net benefits (consumer surplus) from their wilderness recreational experience, or an average of $29.38 for each individual's visit, over and above the cost of traveling to the wilderness area. Based on the estimate that the Weaverville data represent 60 percent of total visitation to the study area, a total of 7,455 people are estimated to have visited the study area in 1999. These 7,455 visitors are estimated to have spent $566,058 in travel cost to access the wilderness experience. These 7,455 visitors are estimated to have received a total of $219,028 in net benefits from their wilderness recreational experience, over and above the cost of traveling to the wilderness area.

As a federally designated wilderness under active management, the study area can be expected to generate a flow of recreational use benefits into the indefinite future. Thus the study area resource can be considered a form of natural capital stock. The economic value of capital can be estimated by adding up the present discounted value of the annual flow of benefits that it generates. There is no absolute rule for selecting a discount rate to value natural capital. Conceptually there are several alternatives. The U.S. Congressional Budget Office (CBO) uses a two percent real discount rate for policies having long-term social implications, which would seem to be consistent here (Bazelon and Smetters, 1999). This two percent rate is considered to be the risk-free time preference of consumption, or the social rate of time preference. The U.S. Forest Service authorizes a four percent real discount rate for analysis of recreational resources (U.S. Forest Service, 1995, p. IV-5). Finally, the U.S. Office of Management and Budget (OMB) directs federal agencies to use a seven percent discount rate in their base-case analysis of proposed public investments (Bazelon and Smetters, 1999). The seven percent real rate is seen as the marginal pre-tax rate of return on an average investment in the private sector in recent years. Thus the recreational value of the natural capital stock in the eastern Trinity Alps wilderness will be estimated using a two, four, and seven percent real discount rate.

If each year into the indefinite future the study area resource will generate $219,028 in (inflation-adjusted) net recreational use value, then as a consol the net recreational use value of the natural capital stock of the study area is estimated to range between $3.13 and $10.95 million. The net recreational use value of the natural capital stock at the intermediate discount rate of four percent is 5.48 million.

The zonal travel cost analysis indicates that visitors receive an average of $29.38 in net benefits, as measured by estimated consumer surplus, from a visit to the eastern Trinity Alps in 1999. It is instructive to compare these findings to other travel cost-based backcountry valuation studies. Englin and Shonkwiler (1995) applied a variant of the TCM using individual visitor survey data to assign an economic value to hiking in the Cascade mountain range of Washington and Oregon. Their preferred estimate was that an average hike generated between approximately $16 and $24 (1985 dollars) in net benefits. Using similar methodology Casey et al. (1995) estimated mean consumer surplus per visit of approximately $513 for hiking in the Grandfather Mountain Wilderness Preserve in North Carolina. This large value for consumer surplus occurs in part because the opportunity cost of time revealed by individual visitors was quite high, averaging nearly $47 per hour. Peterson and Arnold (1987) used the zonal TCM to estimate the net economic value of participation in the Pikes Peak Marathon, an event in which runners traverse miles of mountain trails from Manitou Springs Colorado to the summit of Pikes Peak. Peterson and Arnold estimated that the average participant received approximately $50 in net economic benefits.

Several factors should be kept in mind when considering the broader implications of this study. First, the Big Bar complex of fires, which occurred in the western end of the Trinity Alps in September and October of 1999, created hazardous breathing conditions and travel restrictions that are likely to have reduced visitation from normal levels. The implication is that the aggregate valuation estimates in this study may be low. In this sense the fire offers a natural experiment on the impacts of adjacent fires on recreational activity, and it would be interesting to repeat the analysis in 2000 in order to quantify fire impacts. Second, the valuations found in this study are limited to recreational use, and do not include passive uses such as existence, option, and bequest values held by non-visitors, nor do they include the value of ecosystem services such as water, air, and wildlife that flow beyond the study area boundaries. In fact, the empirical literature suggests that the sum of existence, option, bequest and ecosystem services value is likely to exceed that of active recreational use (Hackett, 1998).

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