United States

Department of

Agriculture

Forest Service

Effective Recreation

Opportunity Set (EROS)

Index: A Computable

Measure of Recreation Supply

Southeastern Forest

Experiment Station

Research Paper

SE-286

Donald B.K. English

H. Ken Cordell

\
The Authors:

DolloldB.K.En#ahisaResearch!hcialScientistandH.Ken

Ctwddl ls Project Leader, Outdoor Recreation and Wilderness

Research Group, Southeastern Forest Experiment Station, USDA

Forest Se&e, Athens, GA.

Acknowledgments:

We thank Mark Hemy (Clemson University), Steve Daniels

(Oregon State University), and Alan Randall (Ohio State

University) for their review comments. This research represents

more than 5 years of data u&ction, theory development, and

analysis by many people.’ Funding from the Program and

Aaftssment Staff of the USDA Forest Service made completion of

the project possible.

March 1993

Southeastern Forest Experiment Station

P.O. Box 2680

Asheville, North Carolina 28802
Abstract

A measure of the supply of recreation opportunities, computable

from available data, is presented in this Paper. The measure is based

on the theory of the household production of recreation supply. It

measures the availability of a set of recreation resources to

households in a given location as an input to producing recreation

trips, relative to the availability of the same set of resources to

households in other locations.

The measure described is developed as an index, to allow for

combining several different types of recreation resources into a more

comprehensive metric of availability of a particular recreation

environment. Recreation supply availability is shown to be positively

related to the amount of resources, and negatively related to both

competing populations and the diitance separating households and

resources The steps taken to calculate 1989 RPA recreation

opportunity indices are described and illustrated with a hypothetical

example.

Keywords: Supply, outdoor recreation, household production theory,

effectiveness.

Introduction

Since the early 1960’s, public policymakers have been

concerned about the adequacy of recreation resources

relative to the demand for the activities (Bureau-of

Outdoor Recreation 1973; Cicchetti and others 1%9;

Cordell and others 1990, Outdoor Recreation Resources

Review Commission 1%2). Related issues include

resource distribution compared with population

distribution, trends in resource availability, comparison

of resource availabiity across regions, and the role of

available recreation opportunities as a recreation

demand determinant. These issues are important in

State and Federal resource planning efforts.

To meet the requirements of the Forest and Rangeland

Renewable Resources Planning Act (RPA) of 1974, the

Forest Service assesses the current situation and projects

future supplies of and demands for renewable resources,

including outdoor recreation. In the most recent RPA

Assessment of Outdoor Recreation and Wilderness

(Cordell and others 1990), demand was analyzed with

the theoretical model of the household production of

recreation trips (Bockstael and McConnell 1981; Cordell

and Bergstrom 1991). To do so, it was necessary to

have a recreation opportunity supply measure that tit

the theoretical model of household production and

allowed comparison of recreation resource availabiity

across locations. Development of such measures had

been stilled by lack of available resource data and

limited applicable theory. It therefore was necessary to

develop a new measure of recreation supply, the

Effective Recreation Opportunity Set (EROS) index, for

the 1989 RPA Assessment. This paper describes the

theory and method used to derive the EROS index.

Major sections of the paper describe:

. the theoretical model for the household production of

recreation and the role of recreation resources

. the salient dimensions of the price of recreation

resources to the household, drawing on recent

measures of recreation supply

b the proposed supply measure and its relation to the

foregoing theory

b an empirical example of a computable recreation

supply measure

. a summary and suggestions for further research.

Theoretical Background

Household Production of Recreation

Over time, households maximize utility gained from

consuming goods and services other than recreation trips

and from recreation trips produced by the household

(Bockstael and McConnell 1981). Number of trips

taken has been shown to be the most appropriate

economic measure of the output produced by the

household (Bockstael and others 1987; McCoMell 1975).

The general form of the weakly separable utility function

is:

where

x, =

Hj =

U = U(X, ,Hj)

vector of nonrecreation goods and services

consumed per year;

vector of the number of recreation trips of

type j produced per year (i= 1,2,...n).

The optimal number of trips of different types is

determined in two stages (Bockstael and McConnell

1981). First, households minimize trip costs for each

trip type. The resulting cost structure is considered

fmed for the entire planning period. Next, optimal

numbers of trips are determined via constrained utility

maximization.

1
Households produce recreation trips by combii

inputs including recreation resources and facilities,

market goods such as gasoline and equipment, and the

household’s knowledge, skills, and time. The production

function for a recreation trip of type j has the general

form:

Hj = hj(\ , E 9 Sj>

where

I

= a production for j;

Vi = variable input vector, including time;

E = household characteristics, including skills,

knowledge, and recreation equipment

owned by the household, such as RV’s,

tents, and skis,

9

= recreation opportunities for activity j, such

as sites, facilities, and resources.

Inverting (2) yields per-trip requirements for inputs

~ = h’j< E, Sl )

where

h’j is the inverse of 9.

Let Pj be the average cost per trip and let Pv be the

vector of prices for variable trip inputs. Then the per

trip cost can be specified as:

Pj = PP;(E,Sj)

By substituting Equation (4) into the usual Marshallian

demands, a household’s demand for recreation trips, Hj,

can be expressed as:

Hi = f(Pv E, $3 Sip Y) (5)

where

si = recreation opportunities for activities other

thanj; ?

Y = annual household income;

E, Sj = defined as before.

Recreation Sites and Prices

The EROS index was designed to measure the general

availability of recreation opportunities that could be

used in Equation (5). Common measures of recreation

resources, such as raw facility counts or facilities per

capita have been shown to be inadequate (Harrington

1987; Randall 1987). Economic concepts of recreation

supply (Clawson 1984, Harrington 1987) can be quite

difficult to calculate empirically. On the other hand,

opportunity indices have been shown to be

computationally efficient in accounting for the spatial

structure of recreation opportunities and households

(Fesenmaier and Leiber 1987, Kim and Fesenmaier

1990). Our plan was to develop a set of opportunity

indices that were based on economic theory, especially

on the work of Harrington (1987).

The household production model includes recreation

sites and resources among inputs. Households do not

‘buy’ a site, but they do pay a cost to acquire its use.

Harrington (1987) called it the ‘effective price’ for a

recreation site. Effective price measures the availability

of a recreation site to a household. That price includes

entry fees, travel costs in both money and time, and

congestion costs in both queuing time and experience

quality.

A site’s location relative to the household determines

the cost of travel to the site, so travel costs are specific

to an origin-destination pair. Entry fees, if any, are

additional costs beyond travel. Travel costs are assumed

to increase with distance. Sites beyond some threshold

distance from the household become too expensive to

use. Threshold distances can vary by trip type.

As the number of users at a site increases, congestion

and queuing combine to reduce trip quality. Activity,

setting, and desired trip quality level determine at what

use level and how quality declines. Converting quality

decline to an equivalent price variation allows congestion

to be treated as a cost and to be included in the

effective price of site use. Congestion costs depend on

the total number of people at the site, the activity, and

site characteristics including size, facilities, and capacity.

Numbers of users at a site depend on the location and

size of population centers within the appropriate

threshold distance and on all other recreation

opportunities serving each of those origins. That is, all

origins and destinations are considered simultaneously in

calculating congestion costs.

Harrington’s effective price has a good theoretical basis

and is a useful indicator of the availability of recreation

opportunities. Effective price is specific to an activity,

desired trip quality level, origin-destination pair, and

2
the distribution of other users and other sites.

Unfortunately, such specificity makes effective price

difficult to use as an aggregate measure of recreation

opportunity availabiity, as specified in Equation (5).

Households face a vast array of prices even for a single

activity, depending on the site and desired trip quality.

Calculation of effective price requires a great deal of

origin-destination data that are largely unavailable. All

sites have different facilities and activity suitability, so

some means of weighting various facilities must be

found in the price calculations. Calculatiug congestion

costs poses the largest problem, because objective

manifestations of congestion are not well documented

for nonwildemess recreation. Still, Harrington’s work

provided guidance for the development of our aggregate

recreation opportunity supply measures.

Effective Recreation Opportunity Set

(EROS)

The EROS measure of recreation opportunity was

developed primarily for use in the 1989 RPA

Assessment of outdoor recreation and wilderness, and

was based on Harrington’s (1987) effective price. * EROS measures the relative availability of recreation

opportunities to households in different locations. Such

opportunities are provided by public agencies and

private entrepreneurs, and are exogenous to the

household’s recreation production function. EROS uses

available resource, population, and location data. In

particular, EROS measures are based on data in the

National Outdoor Recreation Supply Information

System, a county-level inventory of resources, facilities,

and services available for public recreation use. Using

county aggregates of resource and population data

precluded calculating origin-specific measures of

recreation opportunity supply as proposed by both

Clawson (1984) and Harrington (1987). An even

distribution of both population and resources within

counties was assumed. These data were combined into

a measure that reflects the cost-increasing effects of

both travel distance and congestion. EROS is originspecific and can be defmed for any activity or setting.

The RPA Assessment classified recreation activities and

settings according to two criteria. First was by resource

base--land, water, and snow-and-ice (USDA Forest

Service 1980). The second criterion followed the

Recreation Opportunity Spectrum concept developed by

the Forest Service to classify its lands according to

accessibility, development, and likely human encounters,

More developed resources like campgrounds, urban

parks, or ski areas are often more easily accessible and

have greater capacity to handle crowds. compared with

less developed resources. The differences in both

development and visitation capacity also suggest

intracategory differences in the factors that determine

congestion. EROS supply measures were developed for

12 distinct recreation environments as suggested in

Cordell and others (1989).

EROS Calculation Method

This section outlines the steps for calculating EROS

indices. Because a number of separate steps and several

generations of acronyms are involved, a flowchart

summarizing both the steps and acronyms is provided in

the appendix.

Step 1

Recreation opportunity supply measures should account

for the effects of likely congestion levels. Harrington

(1987) noted that “[resources] per capita might be a

rough indicator of crowdedness at recreation facilities.

An increase in population in a county leads to an

increase in users competing for the recreation resources,

increased congestion, and reduced availability of

recreation opportunities. The first step in the EROS

calculation is to divide county-level resource amounts by

the county population, resulting in a series of resource

per population (RPP) variables.

Step 2

Recreation opportunities for any activity can seldom be

fully measured by one resource. Backpacking

opportunities, for example, depend on acres of forest

land, miles of trails or primitive roads, and numbers of

trailheads providing access to the trails. Additionally,

numbers of guide, outfitter and rental enterprises

enhance resource accessibility by providing knowledge,

organization, and equipment. The problem is one of

combii several different inputs measured in different

units into a single metric of effective opportunities for

one type of recreation. No guidance exists as to the

“correct” proportions of inputs needed to produce or

measure recreation opportunities.

3
Our solution was to transform RPP’s into resource

availability indices to make units comparable. Index

values ranged from 0 to 100. Such indices allow

comparisons of relative abundance of opportunities

across counties. The methods could be duplicated in

subsequent years using the 1989 index base to measure

trends in effective recreation opportunities. Maximum

county RPP values were truncated at the 95th percentile

to account for highly skewed values, and RPP’s were

indexed to that maximum.

Step 3

An expert panel of 20 recreation researchers and

managers was surveyed to assign weights to each RPP

index as a recreation opportunity measure for each of

the 12 recreation environments. Resources central to a

recreation environment, such as wilderness acres for

remote land opportunities, were given a weight of 3.

Resources that provided access to the central resources,

such as boat ramps, trailheads, or guide services, were

assigned a weight of 1. For each county, 12 recreation

opportunity indices (ROI) were calculated as:

ROIi = ~[RpPj *Wij]/ 2=Wij

where

ROIi = recreation opportunity index for category i

(i= 1,2...12)

RPPj = resource per population index for resource

j

wij = expert opinion weight for RPPj in category

i

The 12 ROI values for each county were themselves

indexed across all counties, where the highest ROI value

for each recreation environment was assigned an index

value of 100. This recreation environment index was the

Weighted Opportunity Set Index (WOSI) for the county. i

WOSI values describe the relative availability of

recreation opportunities within a county and allow

comparison of recreation opportunities across counties.

Step 4

WOSI values do not account for all recreation

opportunities available to households. Intercounty travel

implies use of resources in nearby counties. Harrington

(1987) felt that households would distribute their use

across all sites to even out congestion costs. We

incorporated that idea, allowing an osmotic flow of trips

from counties with different resource availabilities. For

example, households in counties with low resource

availability (low WOSI values) will go to nearby counties

with higher availabiity because sites there should be less

congested. Overall, effective recreation opportunity for

households in one county will be increased (decreased)

if nearby counties have relatively greater (lesser)

opportunities.

The magnitude of the effect of a nearby county on

recreation opportunities is determined by the distance

separating the counties and the type of opportunity.

Empirical research (Cordell and English 1985) has

shown that there are differences in household travel

patterns for different activities. It was assumed that

each WOSI could have a unique threshold (maximum)

distance, and that any counties within the threshold

distance could affect the recreation opportunities

available to a household.

The threshold distance for each recreation opportunity

type was estimated in the following manner. An expert

panel of recreation researchers estimated the proportion

of recreation trips for 50 activities occurring in each of

the 12 recreation environments. Trip data from the

19851987 Public Area Recreation Visitor Study were

weighted by these proportions and classified by primary

trip activity. Weighted trip data provided a distribution

of visitor travel distances. It was assumed that the

highest 15 percent of travel distances represented

vacation travel. Clawson (1984) deleted vacation travel

from his effectiveness calculations because one of the

unique characteristics of vacations is the desirability of

long travel. Vacation trips were deleted here as well.

Travel distance at the 85th percentile of each recreation

environment was assumed to be the threshold distance

for that environment. Threshold distances ranged from

40 miles for developed water resources to 250 miles for

developed snow activities (primarily skiing).

The magnitude of the opportunity effect of counties

within the threshold declines with distance. More

distant resources are less important to effective

recreation opportunity supply because they require

higher travel costs. Travel cost models assume that

travel costs rise linearly with distance (Clawson and

Knetsch 1966, Walsh 1986). Effectiveness of resources

was assumed to decline linearly with distance, and to

vanish at the threshold distance. Distances between

counties were measured from county centers. The

4
effectiveness decay weight (EWJ for each opportunity

set i between any two counties x and y was dcfmed as:

EWi, = lw CDq ln>i) ifD,~ TD,

EWti = 0 ifD,> TD,

where

Dv = distance between counties x and y

mi = threshold distance for opportunity set i.

Step 5

The Effective Recreation Opportunity Set (EROS) index

for a county is based on WOSI values, threshold

distances for recreation environments, and effectiveness

decay weights between counties. For any county x,

EROS values were calculated as:

c ( wosr,*Ew~)

EROSi, = y

-h

i=1,2,.. (7)

Y

where

EROS, = EROS value of recreation environment

i for county x

WOSIi, = WOSI value of recreation environment

i for county y

EW& = effectiveness decay weights between

counties y and x for recreation

enviromnent i.

For any county, the most important determinants of

EROS values are the resources available in that county.

Proximity to a county with a large resource mass may

greatly augment effective supply. Similarly, proximity to

other counties with large population concentrations and

few resources will reduce effective opportunities when

these competing populations are taken into account.

Small counties have larger adjustments from

surrounding counties because of greater effectiveness

weights associated with the surrounding counties.

recreation opportunities in modeling amural recreation

trip demand and consumption and the value of outdoor

recreation trips (Bergstrom and Cordelll991; Cordell

and Bergstrom 1991).

Empirical Example

Consider an area comprised of nine square counties,

numbered 1 through 9 (fig. 1). County numbers appear

in the bottom left corner of each county and centers are

marked by asterisks. Let each county be 900 square

miles in area. We will develop an EROS measure for

each county for water-based recreation. Let each county

contain three relevant recreation resources: (1) acres of

lakes, (2) numbers of boat launch ramps, and (3) miles

of lakeshore. The amounts of resources aud population

in each county are shown in table 1. It is assumed that

county 6 is devoid of lakes, and hence of both boat

ramps and lakeshore miles.

*

1

c

4

*

7

c

2

*

6

c

a

Figure 1 - Layout of hypothetical counties.

c

3

c

6

c

9

EROS values have been used to compare the relative

abundance of effective supply of different types of

recreation opportunities across regions and to track the

anticipated future changes in recreation supply

availability (Cordell and others 1990). EROS values

have also been used as regressors representing substitute

5
Table l--Resource and population amounts for empirical

example counties

Acres of Number of Miles of Population

County lakes (1OOOs) boat ramps lakeshore (1~)

15

2 0

10

50

40

0

im

70

50

5

10

15

25

20

0

80

35

50

60

40

100

254

160

0

440

230

225

75

75

150

25

40

20

m

10

25

Step 1

Resource per population values for lake acres (RPPl),

boat ramps (RPP2), and lakeshore miles (RPP3) are

shown in table 2. County 8 has the greatest availability

of both lake acres and lakeshore miles per capita.

County 7 has the greatest per capita avaiIabiity of boat

ramps.

Table 2--Resource per population (RPP) values and

indices, example data

County

Values Indices

RPPl RPP2 RPP3 RPPl RPP2 RPP3

0.20 0.07 0.80 2.9 1.8 3.5

0.27 0.13 0.53 3.9 3.3 2.3

0.07 0.10 0.67 1.0 2.5 2.9

2.00 1.00 10.00 28.6 25.0 43.5

1.00 0.50 4.00 14.2 12.5 17.4

0.00 0.00 0.00 0.0 0.0 0.0

6.00 4.00 22.00 85.7 100.0 95.7

7.00 3.50 23.00 100.0 87.5 100.0

2.00 2.00 9.00 28.6 50.0 39.1

Step 2

Step 3

The central resource for this recreation opportunity is

acres of lakes. It was assigned a weight of 3. Both boat

ramps and lakeshore miles provide access to the water,

and each was given a weight of 1. The sum of ah

weights equals 5. Recreation opportunity indices (ROI)

for counties range from zero for county 6 to 97.5 for

county 8 (table 3). In general, the RPP index of the

central resource determines the ROI values. For eight

of the nine counties, ROI values are within 5 points of

the RPP index level of the central resource. The

relative abundance of lakeshore miles and boat ramps in

county 9 increases the overall ROI value almost 7 points

above the RPP index for lake acres. WOSI values for

each county are created by indexing ROI values to the

largest ROI value for ah counties (table 4). Values

range from zero to 100.

Step 4

Distances between county centers are presented in table

5. Distances range from 30 miles to 84.8 miles. For

this example, let the threshold distance for water

recreation be 45 miles. This implies that the EROS

value for any county wiII depend on its own WOSI value

and the values of only those counties that adjoin it.

Effectiveness decay weights between pairs of counties

have been calculated according to the formula given

previously and are shown in table 6.

Table 3--Resource Opportunity Index (ROI) calculation,

example data

County RPPl l wt1 t RPP2 * wt2 t RPP3 l wt3/5 = ROI

1 2.9 3 1.8 1 3.5 1 2.8

2 3.9 3 3.3 1 2.3 1 3.5

3 1.0 3 2.5 1 2.9 1 1.7

4 28.6 3 25.0 1 43.5 1 30.9

5 14.2 3 12.5 1 17.4 1 14.5

6 0.0 3 0.0 1 0.0 1 0.0

7 85.7 3 100.0 1 95.7 1 90.6

8 100.0 3 87.5 1 100.0 1 97.5

9 28.6 3 50.0 1 39.1 1 35.0

Due to the small number of counties in the example,

RPP values were not truncated. Index values were

calculated based on the absolute maximum RPP values.

Indices for each resource are ako shown in table 2.

6
Table C-Weighted Opportunity Set Index (WOSI)

calculation, example data

County (ROI / MAXROI) * 100 = WOSK county EROS

1 2.8 97.5 2.9

2 3.5 97.5 3.6

3 1.7 97.5 1.7

4 30.9 97.5 31.7

5 14.5 97.5 14.9

6 0.0 97.5 0.0

7 90.6 97.5 92.9

8 97.5 97.5 100.0

9 35.0 97.5 35.9

Table 5--Mileage between county centers, example data

County 1 2 3 4 5 6 7 8 9

1 0.0

2 30.0 0.0

3 60.0 30.0 0.0

4 30.0 42.4 67.1 0.0

5 42.4 30.0 42.4 30.0 0.0

6 67.1 42.4 30.0 60.0 30.0 0.0

7 60.0 67.1 84.8 30.0 42.4 67.1 0.0

8 67.1 60.0 67.1 42.4 30.0 42.4 30.0 0.0

9 84.8 67.1 60.0 67.1 42.4 30.0 60.0 30.0 0.0

Table 6--Effectiveness decay weights between county

pairs, example data

County 1 2 3 4 5 6 7 8 9

1 1.00

2 0.33 1.00

3 0.00 0.33 1.00

4 0.33 0.06 0.00 1.00

5 0.06 0.33 0.06 0.33 1.00

6 0.00 0.06 0.33 0.00 0.33 1.00

7 0.00 0.00 0.00 0.33 0.06 0.00 1.00

8 0.00 0.00 0.00 0.06 0.33 0.06 0.33 1.00

9 0.00 0.00 0.00 0.00 0.06 0.33 0.00 0.33 1.00

Step 5

EROS values for each county are presented below.

9.0

5.6

2.2

35.2

26.4

11.1

79.9

70.8

40.7

EROS values were calculated by:

2 (hwq*l3v,)

EROS, = Y-l

where

EROS,

wos5,

Ewv

= EROS water recreation value for

county x

= WOSI value for county y

= effectiveness decay weight between

counties y and x.

EROS values range from about 2 to almost SO. The

effect of the EROS calculation is to even out disparities

across counties in the within-county availability, the

WOSI values. The seven counties with the lowest WOSI

values show increases in recreation availability when

opportunities in nearby counties are included. Similarly,

the two counties with the highest within-county

availability show reduced availability when use pressures

from nearby counties are taken into account. The

greatest adjustment to within-county resource availability

comes for counties whose neighbors have the greatest

difference in resource avaiIabiIity. County 8 ranked

highest in its within-county availability but dropped to

second in EROS value because of its proximity to

counties 5 and 6, which are relatively much worse off.
Conclusion

The EROS supply measures developed in this Paper are

based on and incorporate existing theory and empirical

research related to outdoor recreation supply. EROS

describes the supply of recreation opportunities specific

to recreation envrronments. By using weighted

combmations of indices, EROS can account for the

variety of resources that make up a particular type of

recreation environment. Analysis could be extended to

include quality and additional capacity measures, as the

available data permit. EROS accounts for effectiveness

of resources, as proposed by Clawson (19S4), by

including both distance measures between counties and

estimation of threshold distances for recreation trips.

Harrington’s (1987) congestion costs are incorporated by

population density weights. EROS measures also could

be extended to include differential congestion effects of

population subgroups on resources. For example,

changes in elderly population may have less effect on

wilderness congestion than would changes in younger

populations.

Further research is needed to define and assess the role

of quality measures for each recreation environment and

the component resources. At present, quality measures

are only marginally included. In addition, research is

needed to validate the resources that describe each

recreation environment and to assess their relative

importance. Fiiy, research should be undertaken to

further develop the estimates of threshold distances and

to test the assumption of a linear decay function for

resource effectiveness.

The primary advantage to EROS over effective price is

that EROS can be calculated from existing resource,

travel, and population data. These two measures are

important advances in economic analysis of recreation

opportunity supply. Combii these with demand-side

developments, especially household production functions

for recreation, provides a sounder base for economic

assessments of outdoor recreation and wilderness.
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Ran&II, A. 1967. Resource economics: an economics approach to

natural resource and environmental policy. New York John

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US. Ikprtmant of Agricultura, Forast Service. 1980. An assessment

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Walsh, RG. 19%. Recreation economic decisions: comparing

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637 pp.

9

APPENDIX

Flowchart for calculating EROS values.

STEP 1 I

Calculate resources

per population (RPP)

STEP 2

STEP 3

I 1

Index RPP values to

95th percentile value

I

Calculate recreation

opportunity index (ROI)

Index ROI values to

get weighted

opportunity set

index (WOSI) values

STEP 4 I

Calculate effectiveness

weights (EW)

STEP 5 Sum weighted WOSI values =

effective recreation

opportunity set (EROS) index

( Resour;qo&ance 1

11

r

---------------------------------------------------------- I 1
The Forest Servlce, U.S. Department of

Agriculture, is dedicatad to the principle of

multiple use management of the Nation’s forest resources

for sustained yields of wood, water, forage, wildlife, and

recreation. Through forestry research, cooperation with the

States and private forest owners, and management of the

National Forests and National Grasslands, it strives-as

directed by Congress-to provide increasingly greater

service to a growing Nation.

,

USDA policy prohibits discrimination because of race,

color, national origin, sex, age, religion, or handicapping

condition. Any person who believes he or she has been

discriminated against in any USDA-related activity should

immediately contact the Secretary of Agriculture,

Washington, DC 20250.