Estimating Social Welfare Using Count Data Models: An Application to Long-Run Recreation Demand Under Conditions of Endogenous Stratification and Truncation

Uses studied:
Place: Cascade Mountains


This study found that surveys that directly extrapolate the number of times an individual person visits a trail to the general population will significantly overstate the future trail use. Care must be taken to account for the differences between those interviewed at the trailhead and the rest of the population.


The methods applied in this paper set the accepted standard for estimating recreational use for the general population based on user surveys at the trailhead. They require specialized statistical skills to apply, and therefore are not going to be usable by most trails advocates. However, the findings are an important reminder for those estimating trail use based on on-site user surveys. As a starting point, advocates can compare demographic information (e.g., age, gender, and income) of the users included in their survey to the demographic information of the broader community of potential trail users.


This study looked at hiking trails throughout the Cascade Mountains of Washington State.

Trail Type

The authors included user and trail data from 25 randomly sampled hiking trails, representing a range of characteristics including elevation, length, the presence of views, total hiking time, the presence of grass and alpine meadows, and the presence of water along the trail.


The purpose of the study was to develop and test a method for predicting long-run visitation of hiking sites using on-site interview data. The study predicts demand across all Washington State residents, not just current users of the trails, addressing a problem of overestimating use when only the most avid users are surveyed. This study was funded by the Sloan Foundation’s Regulation of Natural Resources Grant to the University of Washington, and research support was provided by the Nevada Agricultural Experiment Station.


The following factors affect the number of times a hiker visits the site: distance from hiker’s home, distance on dirt road to reach the trailhead, presence of water, high-point elevation, and presence of alpine meadows. Findings showed:

  • Fewer visits the further the trail is from the hiker’s home (0.24 fewer trips every 10 years for every additional 10 miles traveled);
  • Fewer visits the further the respondent had to drive on a dirt road (0.08 fewer trips every 10 years for every additional mile of dirt road to reach the trailhead);
  • More visits if there is water along the trail (0.9 additional trips every 10 years if there is water present);
  • More visits the greater the trail’s high point elevation (0.6 additional trips every 10 years for every thousand feet increase in the trail’s high point);
  • More visits for the presence of alpine meadows (0.5 additional trips every 10 years if alpine meadows are present along the trail); and
  • No difference in visits for the number of people the respondent expected to encounter.

Those surveyed at the trailhead use the trail more than four times as often as the general population, with trail users visiting an average of 2.11 days over ten years versus 0.49 days over ten years for the general population.


Data for hikers were obtained from an on-site survey implemented at 25 random trails in the Cascade Mountains. They included only respondents for whom hiking was the primary purpose, and who lived in Washington State. Respondents were asked questions about how often they hiked the trail and demographic information. Data for trail characteristics were gleaned from trail descriptions in published guidebooks. To estimate the number of trail users, the researchers used a statistical model known as a count data model. Using demographic information, this model accounted for the fact that the respondents they interviewed at trailheads are likely more frequent hikers than the average Washington resident. They use these estimates for demand to calculate individuals’ expected number of hiking trips in the Cascade Mountains over a 10-year period.

This study relied on the same data as Englin and Mendelsohn (1991), but estimated factors affecting levels of trail use rather than spending for users on different trails.


Englin, J. and J. Shonkwiler. 1995. “Estimating social welfare using count data models: an application to long-run recreation demand under conditions of endogenous stratification and truncation.” The Review of Economics and Statistics 77(1): 104-112.