United States 

Department of 

Agriculture 

Forest Service 

Southern Research 

Station 

Research Note 

SRS-2 

June 1996 

Assessing Regional Economic 

Impacts of Recreation Travel 

from Limited Su ey Data 

Donald B.K. English and Jean-Claude Thill 

Abstract 

Regional economic impacts of public recreation facilities are caused by 

purchases made by households during trip production. Purchases are made 

near home, en route, or near the recreation site. Locations where en route 

purchases are made are particularly ill-defmed. Surveys that gather trip 

expenditure data usually only collect home and site locations and travel 

mileage, with no reference to the actual route taken to the recreation site or 

where en route purchases are made. The elliptic method uses current survey 

data to estimate the amount of en route purchases made in any location as a 

function of the likelihood of travel through that location. The purchase 

estimates are then aggregated at the level of codes or groups of counties 

designated in the economic impact analysis. 

Introduction 

Public land management agencies are increasingly interested 

in assessing the regional economic impacts of recreation trips 

to their lands. These hpacts are caused by money spent in 

the local economy by households producing recreational trips 

(Dean and others 1978, English and Rergstrom 1994, Lieber 

and Allton 1 983). Special attention has been grven to small, 

often rural, mdti-county economies around those public lands. 

A primary reason for hs interest is to evaluate whether 

recreation can be used as a strategy for rural development and 

income redistnibution @erg&orn and others 1990). 

Donald B.K. English is Research Econ~~st, Southem Research Station, 

USDA Forest Service, 320 Green Street, Athens, 6.4 30602-2044; and JeanClaude Thi11 is Associate Professor, Department of <ieogaphy, University of 

Georgia, Athens, GA 30602-2502. 

To complete their economic impact studies, public agencies 

usually gather data using detailed user surveys. Current 

survey instruments are primarily concerned with the dollar 

mounts of purchases of different types of goods and services 

by visitors and pay little attention to spatial aspects of either 

the trip or the purchases (Propst and others 1985). 

Commonly, spatial data on the trip are limited to identwg 

starting and ending points and total mileage traveled. The 

route actually followed by the household to reach the 

recreation site is unknown. Similarly, locational information 

for expenditures is often no more than whether each purchase 

was made in the hometown, en route to or fkom the recreation 

site, or at the site itself. Thus, locations for purchases made at 

home or at the site are reasonably well defined, while locations 

for en route purchases are not. Purchases made while 

traveling can account for a si@icant portion of total trip 

expenditures, particularly for short-term visits (JEnglish 1 992, 

Stevens and Rose 1 985). 

The lack of geogaphic content in travel expenditure data 

precludes a direct assessment of the economic impact of en 

route purchases on regional economies. Analysts must rely on 

indirect methods to estimate the mount spent by each 

surveyed household on en route pmchases occunring in the 

regional economy studied. For the remainder of the paper, we 

use the tenn "region" to mean the geogaphc area that 

contains the economy and "mount" to indicate the dollars 

spent on purchases. 

We assume that the expected mount of purchases that a 

household makes in a regron whle traveling to or from the 

reereation site is directly related to the mount of recreation 

travel that occurs in the regron. No purchases will occur in the 

regron if the household does not travel through it. At the other 

extreme, if all travel occurs in the regron, all purchases 
made while traveling must be made there. In. fi 

ation, an equiproportionality relationship can be 

posalated. 

Cmenay, public agencies use a simple, but ad hoc method to 

spatially allocate purchws. This methd wsumes that the 

proportion of en route purchases made in the region is the 

same w the proportion of the straight-line distance from home 

to the recreation site that lies within the region @ergstrom and 

others 1990, English 1992). This method makes two 

impomt assmptions. First, that households only travel in a 

straight line from home to the recreation site. Second, that the 

probability of travel through each point on the line is dorm. 

Our method relaxes both assmptions and makes use of two 

additional pieces of Somation: the actual distance the 

household travels and the shape of the region. 

Our main objective was to develop a procedure (elliptic 

method) that uses more of current survey data (to estimate 

expendimes in a region). In the: followhg sections we present 

the theoretical backdrop to the problem, dekbe the 

procedure for cajculating the expected proportion. 

(probability) of recreation travel through a spatial area, grve 

an empirical example, and provide conclusions. 

Theoretical Backdrop 

Household production of recreation trips provides the 

economic basis for regional economic impact analysis 

(English and Bergstrom 1994). Households combine 

purchased market inputs with their skills and time to produce 

and consume trips. Within this context, households attempt to 

minimize the costs of producing recreation trips (Bockstael 

and McGome11 198 1). These costs include the prices paid for 

goods and services used during the trip, such as lodging, site 

entry, or equipment. The costs of while traveling 

to and from the site, such as food, gasoline, and ldging, and 

the value of the household's time for traveling and acq~g 

the purchased goods are also included (I3ockstael and others 

1 987, Clawson and Knetsch 1 966). Thus, ing trip 

prduction costs entails *kg the time and money costs 

both of the actual travel and of shopping for and acquiring all 

inputs (I,entnek and others 1987, Wihan 1980). 

The most cornonly p during the travel phase 

of the recreation trip, food and gasoline, are moderately priced 

and easily obtained. These characteristics imply hghly 

restricted price search and shopping efforts by households in 

both time and space, because shopping costs soon outweigh 

price savings (Eaton and Lipsey 1 979). Limited shopping 

eEort hplies that (1) purchases made during travel will occur 

along the travel route, and (2) the choice ofthe opbal (least 

cost) travel route will p and be independent of en route 

purchase decisions. Potential savings on en route pwchases 

are not worth simcasrt shopping effort, and are thus 

conditional upon travel route choice. 

Travel to the recreation site is necessq- for trip production. A 

route beween home and recreation site that -es the 

generalized travel cost, which is a weighted sum of the 

monetized value of distance and time, is chosen. Given a 

featueless plain, households would certainly elect to dnve 

directly to the site. However, the usual circuity of roads makes 

straight-line travel unlikely. Moreover, mum mileage 

routes may not be the fastest routes. Congestion and speed 

limits may make longer routes less expensive when 

considering the value of travel time. Therefore, possible travel 

routes are distributed about the straight line from home to the 

reereation site. However, as the household tries to minimize 

its total travel costs, the likel&ood that a route is selected away 

from ths line decreases. 

Calculating Expected Travel Proportion 

In this section, we construct the probability distribution 

functions of traveling through any location, given the limited 

data collected in user surveys: the origin, destination, and 

length of the trip. From these functions we derive the 

expected proportion of recreation travel through any defined 

region. 

Consider a household taking a trip fi-om its home, I, to 

recreation site, R, separated by some distance, S. The 

household chooses a gmeralized-cost-*ing travel route 

of length T, where T > S. The envelope of possible travel 

routes of length T is an ellipse whose foci are at I 

and R. 

Several general obmatiom can be made about the travel 

routes ~W the elliptical envelope. In the absence of 

external Somartion (such as road locations or what route the 

household traveled), the distribution of possible travel routes 

will be metrical with respect to both the major and minor 

axes of the ellipse. The number of unique paths through 

locartions along any line dram perpendicular to the major axis 

between the foci of the ellipse decreases away from the axis. 

The nmbm of routes through locations outside the foci 

declines rapidly with distance away from the focal point. Any 

location at the border of the ellipse will be on a single route, 
Figure 1-Example of elliptical travel envelope. 

consisting of travel dxectly to that point &om home and then 

directly to the recreation site. 

For example, let a household be located at the origin, and (S, 

0) be the location of the recreation site. ' The household 

travels an actual &stance, T. Recreation travel is bound to 

occur within an ellipse whose foci are (0,O) and (S, 0) (fig. 1). 

The goal is to calculate the probability that the household 

travels through some location, %,Yo). 

The travel distance, T, is also the straight-line distance from 

home to a point on the ellipse border and then to the recreation 

site. Let I3 be half the length of the minor axis for the ellipse, 

and A be half the straight-line distance between foci, or S12. 

The ellipse is centered around the point (A, O), and (A, B) is a 

solution to the ellipse. The distance from (0,O) to (A, B) is 

T12. Using the Pythagorean Theorem, 

and rearranging yields 

h the general case, the locations of the househoId and meation site could 

be anywhere. However, coordinates can be tmm&omed to make the e 

case applicable. The procedures can be found in analytic geometry texts. 

the equation for the ellipse is 

For any X between (A-(T12)) and (A+(T12)), two Y values 

solve the ellipse. One, Y', will be greater than zero, and the 

other, Y-, will be less than zero. These Y values are: 

Equations (4) and (5) define the elliptical envelope of possible 

routes of length T. This ellipse can be divided into three 

portions. The central portion includes all points lying between 

the foci, i.e., all points where the X coordmate is betureen 0 

and S inclusive. The household must travel through this area 

to get from its home to the recreation site. The remaining two 

portions lie between the foci and the two end points, where 

either X < 0 or X > S. The household may choose to travel 

through these areas, but need not do so. 

Now we investigate the pattern of trips wih the defined 

elliptical envelope. For the central portion of the ellipse, we 

assume the likelihood of recreation travel through a point 

Mt.ithin thts portion, (&,Yo), is distributed normally along the 

line perpendicular to the X axis. The probability of travel 

through that point, pr (&,Yo), is: 

where cr is the standard deviation. 

Wfule Yo is known, the value of the standard deviation must 

be determined before the probability can be calculated. We 

assune that, for any X between 0 and S, the ellipse border is 

four standard deviations from the X axis. Because the 
absolute vertical distance to the ellipse, Yi in equation (4), is 

gteatest at A and declines as X approaches either 0 or S, a is 

Calculating the probability of recreation travel through any 

point in this portion of the ellipse is now possible by 

substituting equation (7) for a in equation (6). 

Households will only enter the end portions of the ellipse if the 

route minimizes generalized costs. The fkther into the end 

portion a point is located, the less likely the household will 

travel through it. As a result, the likelihood of travel through a 

point in an end portion of the ellipse depends on both the 

way from the major axis, and on its 

horizontal distance away from the central portion of the 

ellipse. In general, because the probabilities for the horizontal 

and vertical distances are independent, the probability of travel 

through a point, (S,,Y,), in one of the end regions is: 

Along the vertical dimension, travel probabilities are still 

assurned to be normally distributed along the line 

perpendicular to the major axis. However, if the standard 

deviation, a, was calculated by the process developed for the 

central portion of the ellipse, the value for a would collapse to 

zero at the end points of the travel ellipse. To prevent 

collapse, we hold a constant for points in the end portion. 

This constant value, a,, is the value obtained for a &om 

equation (7) when X = 0. 

For the hokntal dimeflsio~ let g(D) denote the probability 

of travel at any horizontal distance, D, into an end portion of 

the ellipse: 

L12 32L12 g(D) = exp [--I = exp [- 

2a2 (T-a2 1 . (9) 

The hction, go), is the normal density function with the 

amstant tm removed, so go) approaches unity as D 

appm~ches zero. The value for a for the horizontal dimension 

is also constant, and set to one-fourth the distan~e from a foeus 

to the nearest end point of the travel ellipse. 

We first consider the left-end portion where X < 0. Let 

(X,,Y,) be a point in the left-end portion. The probabiiiy of 

travel through (X,,Y ,) is: 

Similarly, the probability of travel through a point in the rightend portion, (X,,Y,), is: 

Now, the two-dimensional travel ellipse is transformed into a 

probability solid, where the height of the surface above any 

point on the X-Y plane is the probability of travel through the 

point as calculated by equation (6), (lo), or (1 I), whchever is 

appropriate. The solid shows the distribution of travel for 

points within the ellipse (fig. 2). The surface is continuous. 

Two spikes of maximum travel probability occur at the foci on 

both sides of the ridge of local maxima saddling the line 

segment connecting foci, the surface height falls 

monotonically. Finally, the height declines rapidly in the end 

portions. 

The process of estimating the expected proportion of travel 

that occurs in the regional economy is analogous to estimating 

the ratio of the volume of a portion of the travel probability 

solid to its total volume, where the portion of interest is the 

intersection of the travel ellipse and the targeted region. To 

complete this process, we calculate the total and travel 

probability masses for each portion of the ellipse. 

The total probability mass for the entire central portion of the 

ellipse is: 

y2 exp [--1dYa'X. 

20; 
Figure 2-Probability of travel within ellipse. 

The total probability mass for the entire left-end portion of the 

ellipse, TOTLEFT, is: 

y2 exp [- (- + - 32x2 )]dYdX. 

20; (T-a2 

And total probability mass for the entire right-end portion. of 

the ellipse, TOTRIGHT, is: 

Let the region, Z, be a copvex set of points in the X-Y plane2 

(fig. 3). Let X' and X, be the &urn and rn-q 

respectively, of the set of X values in the intersection of the 

travel ellipse and Z. ?is interation is the shaded area in 

figure 3. Also, let Y, be the "top" of the intersection of Z 

and the travel elhpse, and Y; be the "bottom," where 

The travel probability for the central region is: 

1 y2 exp [--]dYdX, 

202 (18) 

1 y2 exp [--1dYdX , 20; (1 9) 

=i 7- 1 exp [--]dm y2 , 

x5Y; Y-r; \I- 20,' (20) 

Ifregion Z is xionconvex, it can be divided into compo& convex sets. The Figure 3-Intersection of region targeted for economic analysis (2) and travel 

pr~canthenh~appli&toeach~n&set. ellipse. 
The travel probabaiv for the portion of Z in the left-errd 

region, PRLEFT, is: 

ifx; < 0 . 

The travel probability in the right-end region, PRRIGHT, is: 

PRRIGNT=O, ifx;<s, (24) 

Thus, for a household I, with total en route trip 

amout of en route pwch8ses made in region 

Z, &, would be: 

Empirical Emmple 

We used travel and trip expenditure data from a sample of 

visitors to five recreation sites during the -er of 199 1. 

The sites included Lo10 National Forest (BAT), Ozark National 

Forest (AR), Yuba Lake Recreation Area (UT), Toiyabe 

National Forest (CMV), and Columbia River Gorge 

National Remeation Area (OWA). We were only interested 

in the behavior of visitors from outside the region, who spent 

some money while traveling. We did not use data from 

visitors who reported traveling more than 1,000 miles to the 

visited site. Mer culling data from visitors with no 

detdable home location, 394 observations remained. 

Two Herat codpations for the econonric regrons 

smomding the recreation sites were ex&&. One was a 

circle of 50-mile radius. The other was a square, oriented 

No&-South, with the same total area as the circular region. 

For nomesidents of each regional configuration, we estimated 

the percentage of trip travel that occurred in the region, for 

both the ad hoc and elliptic methods (table 1). Estimates of 

trip expenditures occurring in the region were derived by 

multiplying reported en route trip expenses by the regional 

travel probabilities. 

Table 1 -Estimated portion of recreation travel occurring 

in target region, by region shape and estimation method 

Finally, the probability of recreation travel wurring within 

the intersection of Z and the travel ellipse is: 

Regional configur~tion 

Estimation method Square Circular 

Ad hoc travel 

Elliptic travel 

Difference 

Percent 

32.5 1 36.90 

29.58 32.58 

2.93 4.32 

Dollars 

Ad hoc travel $25.57 $28.72 

Elliptic travel 23.27 25.3 1 

Diffaam 2.30 3.41 
The ad hoe me&& allocated a greater proportion of rareation 

travel to the target region than the elliptic method. DifFerences 

across the two methclds averaged 3 to 4 percent, depading on 

the shape ofthe target region. Gomp g the me&ods Ebr m 

hegulwly shaped region could result in even @eater 

differences. 

On the average, nonresidents of the example regons reported 

spenhg slightly less than $80 while traveling. As calculated 

by equation (28) and depending on the method 

region shape, we eshated that visitors spent between $23 

and $28 in the region while traveling to the site they visited. 

The percentage differences across the methods translate into 

expenditure differences of $2.30 or $3.41 per visitor. 

Conclusion 

Travel is a necessary part of recreation trips. The mount of 

en route purchases a household makes in a certain region 

depends on the probability of travel through the region. lks 

paper reported a method for estimating the expected momt of 

recreation travel through a region, given the limited mount of 

trip travel data often collected in visitor surveys. 

Our elliptic method represents an improvement over the ad 

hoc methods currently used for estimating the proportion of en 

route purchases occurring in a region, although it requires no 

additions to current survey instruments. Less restrictive 

assumptions about recreation travel are required compared to 

the current method. In addition, our method both makes use of 

and is sensitive to the ratio of actual to straight-line travel 

distances and to the shape of the region. 

The results indicate that this new method yields more 

conservative estimates of the amount of recreation travel and 

associated purchases that occur in a region. Incorporating this 

method into procedures used by public land managing 

agencies, such as the USDA Forest Senrice, to estimate 

regional economic kpacts ofrareation can be readily 

accomplished. Future research should iacorporate information 

on the number and types of purchase opp 

in estimating en route expendrtures. Travel Ihrough a region 

is a neGessary but not sufficient condition for malung en route 

purchases in that region. Purchase oppo-ties must also 

exist. However, only limited hprovements to the method 

proposed here are possible without frrst increasing the quality 

and quantity of trip domation contained in user surveys. 

Acknowledgment 

The authors thank Roderick Knapp: Jeffery Dorfnzm, and John 

Bergskom for their assistmm in clfiing ideas and concepts 

in this paper. 
Literature Cited 

0-&KE. 1981. Theory& 

hdion for WiIdlZe rw&ion. Journal of 

es and Mmgm& 8: 199-214. 

N.E.; Stmd, I.E.; H W.M. 1987. Time and the 

recreation -d model. American Journal of Agriculmal Economics. 

69: 293-302. 

on, M.; Knetsch, J.L. 1966. Economies of 

mm: Job Hopkins Press. 

G.M; Letx, M; Nehn, I^; Sei-id, J. 1978. The local economic 

impact of state parks. Joumal of Leiare Research. 13: 98-1 12. 

Eaton, B.; Lipsey, R 1979. Comparimn shopping and the clustering of 

homogeneous firms. Journal of Regional Science. 19: 42 1-43 5, 

English, D.B.K. 1992. Theory and techniques for estimhg regional 

economic impacts from outdoor recreation visitor 

GA: University of Georgia. Ph.D. dissertation. 

B-IG; Bemew J.G. 1994. The wnq-1 

on facility develop& and regid economic of 

Regioml Skmm. 34 (4): 599-6 1 1. 

SC. 1987. 

in economi 

Wmfiy. 62: 334-348. 

act 

Venture Publishing Inc.: 36-54. 

Propst, D.B.; Gavrh, D.G.; Cordell, H.K; Hansen, W.J. 1985. 

sm: 

Ew& Station: 52-63. 

Stevens, B.; Rose, A. 1985. Regional inputsutput methods for tourism 

impact analysis. Propst, D.B., ed. of 

recreation and tou 

For& Service, So 

I3.A 1980. The value of time in recreation benefit studies. Journal 

of Environmental Economics and Management. 7: 272-286. 

The United States Department of Agriculture 

(USDA) prohibits discrimination in its progrms on the basis of 

race, color, national origin, sex, religion, age disability, 

political beliefs and marital or familial status. (Not all 

prohibited bases apply to all programs.) Persons with 

disabilities who require alternative means for communication 

of program information (braille, large print, audiotape, etc.) 

should contact the USIM Office of Communications at (202) 

720-2791. 

To file a complaint, write the Secretary of 

nt of Agriculture, Washington, DC 

20250, or all (202) 720-7327 (voice) or (202) 720-1 127 

(mD), USDA is an equal employment oppm;inity employer. 

Southern Research Station, P.O. Box 2680, Asheville, NC 28802