• TABLE OF CONTENTS
HIDE
 Front Cover
 Abstract
 Acknowledgement
 Table of Contents
 Introduction
 Model development
 The statistical models
 The estimated models
 Inferences from the estimated...
 Summary and conclusions
 Reference
 Statistical appendix














Group Title: Economics report - University of Florida. Agricultural Experiment Station ; no. 104
Title: Demand for recreational facilities
CITATION THUMBNAILS PAGE IMAGE ZOOMABLE
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00027713/00001
 Material Information
Title: Demand for recreational facilities a methodology and its application to camping
Series Title: Economics report
Physical Description: iii, 59 p. : ; 28 cm.
Language: English
Creator: Gibbs, Kenneth C
Publisher: Food and Resource Economics Dept, University of Florida
Place of Publication: Gainesville Fla
Publication Date: 1981
 Subjects
Subject: Camp sites, facilities, etc -- Economic aspects -- Mathematical models -- Florida   ( lcsh )
Camp sites, facilities, etc -- Public use -- Mathematical models -- Florida   ( lcsh )
Recreation areas -- Economic aspects -- Mathematical models -- Florida   ( lcsh )
Recreation areas -- Public use -- Mathematical models -- Florida   ( lcsh )
Demand (Economic theory) -- Mathematical models   ( lcsh )
Genre: government publication (state, provincial, terriorial, dependent)   ( marcgt )
bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Bibliography: Bibliography: p. 52-53.
Statement of Responsibility: Kenneth C. Gibbs, Thomas A. Jennings.
General Note: Cover title.
General Note: "December 1981."
 Record Information
Bibliographic ID: UF00027713
Volume ID: VID00001
Source Institution: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: aleph - 002199022
oclc - 21028180
notis - ALD8902

Table of Contents
    Front Cover
        Front Cover
    Abstract
        Page i
    Acknowledgement
        Page i
    Table of Contents
        Page ii
        Page iii
    Introduction
        Page 1
        Page 2
    Model development
        Page 3
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
    The statistical models
        Page 16
        Page 17
        Page 18
        Page 19
        Page 20
    The estimated models
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
    Inferences from the estimated models
        Page 28
        Page 29
        Page 30
        Page 31
        Page 32
        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
        Page 38
        Page 39
        Page 40
        Page 41
        Page 42
        Page 43
        Page 44
        Page 45
        Page 46
    Summary and conclusions
        Page 47
        Page 48
        Page 49
        Page 50
        Page 51
    Reference
        Page 52
        Page 53
    Statistical appendix
        Page 55
        Page 57
        Page 59
Full Text

December


1981


Economics Report 104


Demand for


Recreational


Facilities:


A Methodology and
Its Application to Camping


Food and Resource Economics Department
Agricultural Experiment Stations
College of Agriculture
Institute of Food and Agricultural Sciences
University of Florida, Gainesville, 32611


/


/


Kenneth


C. Gibbs


Thomas A. Jennings


~
I


I


i













ABSTRACT


Theoretical and empirical models of recreation demand were developed
and estimates for camping generated from the empirical models in Florida
state parks. Development of the theoretical model leads to criteria fa-
voring the recreationist's variable daily on-site cost as the proxy price
for recreational facility use. Applicability of the models in analyzing
demand of the multiple-destination recreationists was achieved by intro-
duction of an adjustment factor applied to travel costs. Some new em-
pirical evidence of the role of leisure-time constraints is presented
which suggests that they are of minor consequence to the recreationist's
demand for particular facilities.

Key words: Economics of outdoor recreation, recreation demand,
Florida--recreation demand.


ACKNOWLEDGEMENTS


The research reported herein was conducted at the University of Florida,

and financially supported by the Florida Agricultural Experiment Stations

through State Project No. AS-01623. Manuscript preparation and secretarial

assistance were performed at Oregon State University.

The publication is based heavily upon Thomas A. Jenning's Ph.D. disser-

tation, "A General Methodology for Analyzing Demand for Outdoor Recreation,

With an Application to Camping in Florida State Parks," Department of Food

and Resource Economics, University of Florida, 1975.

The authors are indebted to countless personnel of the Florida Depart-

ment of Natural Resources for the data supplied, expert advice, and unhesi-

tating willingness to share their information.

The authors gratefully acknowledge the review comments and helpful sug-

gestions of William G. Brown, Ronald A. Oliveira, Roy Carriker, and Thomas

H. Spreen.













ABSTRACT


Theoretical and empirical models of recreation demand were developed
and estimates for camping generated from the empirical models in Florida
state parks. Development of the theoretical model leads to criteria fa-
voring the recreationist's variable daily on-site cost as the proxy price
for recreational facility use. Applicability of the models in analyzing
demand of the multiple-destination recreationists was achieved by intro-
duction of an adjustment factor applied to travel costs. Some new em-
pirical evidence of the role of leisure-time constraints is presented
which suggests that they are of minor consequence to the recreationist's
demand for particular facilities.

Key words: Economics of outdoor recreation, recreation demand,
Florida--recreation demand.


ACKNOWLEDGEMENTS


The research reported herein was conducted at the University of Florida,

and financially supported by the Florida Agricultural Experiment Stations

through State Project No. AS-01623. Manuscript preparation and secretarial

assistance were performed at Oregon State University.

The publication is based heavily upon Thomas A. Jenning's Ph.D. disser-

tation, "A General Methodology for Analyzing Demand for Outdoor Recreation,

With an Application to Camping in Florida State Parks," Department of Food

and Resource Economics, University of Florida, 1975.

The authors are indebted to countless personnel of the Florida Depart-

ment of Natural Resources for the data supplied, expert advice, and unhesi-

tating willingness to share their information.

The authors gratefully acknowledge the review comments and helpful sug-

gestions of William G. Brown, Ronald A. Oliveira, Roy Carriker, and Thomas

H. Spreen.









TABLE OF CONTENTS


Page

ABSTRACT. . . . . ... . . i

ACKNOWLEDGEMENTS . . . . ... . i

LIST OF TABLES. . . . . ... .. iv

LIST OF FIGURES . . . .... .... .iv

INTRODUCTION . . . . . 1

MODEL DEVELOPMENT . . . . ... .. 3

Antecedents. . . . . ... .. 3

Direct Methods. . . . ... ... 3
Indirect Methods. . . . . 4

The General Theoretical Model. . . . 7

Choice of a Proxy for Facility Price . . 8

The Inappropriateness of Travel Cost as the
Proxy . . . . . . 9
Composite Prices, Ideal Proxies, Site
Specificity, and On-Site Cost . . .... 10
The Conceptual Model with On-Site Cost the
Choice of Proxy . . . . .13

Sample Data. . . . . ... ..... 14

THE STATISTICAL MODELS. . . . . ... 16

Definition of Variables. . ..... . 16

Choice of Equation Form. . . . ... 19

THE ESTIMATED MODELS. . . . .... 21

Length-of-Stay Equations . . . .... .21

Frequency-of-Visits Equations .. .. ..... 24

A Note on Leisure Time Constraints .. ........ .26

INFERENCES FROM THE ESTIMATED MODELS. . . .. 28

Use as a Function of Travel Cost . . .... 28









Page

Use as a Function of On-Site Cost. . . .. 30

The Equations . . . . 30
Implications for Aggregate Demand . . .. 34

Use as a Function of Seasonal Change . ... .35

Estimation of Recreation Value . . .... .36.

Value Received from Northern Parks. . . ... 38
Value Received from Southern Parks ........ . 42
Illustration of a Value-Based Fee Policy. . .. 43

SUMMARY AND CONCLUSIONS. . .... . .47

Summary . . . . .... 47

Conclusions . . .... . . 48

Limitations . . .... . . 49

REFERENCES . ..... . . . 52

STATISTICAL APPENDIX: Mean Values of the Variables
for the Samples of Florida State Park Campers, 1973. 55

Correlation Ni'trix: Northern Parks ...... .. 57

Correlation Matrix: Southern Parks ...... .. 59













DEMAND FOR RECREATIONAL FACILITIES:
A METHODOLOGY AND ITS APPLICATION TO CAMPING


Kenneth C. Gibbs and Thomas A. Jennings


INTRODUCTION

Few would dispute the therapeutic and other intangible benefits of rec-

reation. Recreation also has economic value, as attested by the fact that

people are willing to pay for it. Interest in its economic value has been

growing as policy makers and planners, especially in the public sector, re-

quire more stringent justification for the increasing costs of land and other

resources that must be combined in order to provide opportunities for high-

quality recreation experiences.

The research on which this study reports was designed to answer questions

such as: Is the value to users of a camping facility high enough to justify

the ever increasing costs of maintaining the parks for campers or building

new camping parks? Can a methodology be developed to accurately estimate

recreationists'response in order to suggest a more rational fee policy? The

methodology developed herein is a general methodology in the sense that it

could be applied to many types of recreational facilities whose use requires


KENNETH C. GIBBS is associate professor in the Resource Recreation Manage-
ment Department, School of Forestry, Oregon State University, Corvallis. He
was formerly associate professor of food and resource economics at the University
of Florida. THOMAS A.JEININGS is currently assistant professor of economics
at the University of Louisville. He was formerly graduate research assistant
in food and resource economics at the University of Florida.








the recreationist to incur tangible cost while actually at the facility.
The specific objectives of the research were to (1) develop a conceptual

model of recreation demand; (2) estimate, on the basis of sample data, the

parameters of a statistical counterpart of the conceptual model; and (3) il-

lustrate applicability of the estimated model to real problems of planning

and management. The discussion that follows is divided into three basic

sections: theory, measurement, and application, in that order. The fourth

and final section summarizes the major conclusions of this research and sug-

gests some topics for future research.










MODEL DEVELOPMENT


It is of limited practical usefulness to discuss the theory of recrea-

tion demand without considering the typical measurement problem arising from

insufficient variation in use fees of many recreation facilities that are

publicly provided. The facility's use fee, U (which may be zero), is all

that can be properly called the facility's own price. In order to estimate

the demand for a facility as a function of its own price, it is necessary to

know a range of prices that the consumer would be willing to pay rather than

surrender his use of the facility. It is thus difficult to estimate the effects

of a fee change directly, except on the basis of the implausible assumption

that consumers' income, prices of alternative forms of recreation, user popu-

lations, etc., do not change over a several year period. Moreover, as a use

fee remains constant, the range of higher prices that would not drive the

average recreationist away from a facility is likely to be significantly above

the actual use fee if only because of general inflation of prices and consumer

incomes.


Antecedents

The literature offers two possible ways of estimating the recreationist's

response to a hypothetical fee change; the so-called "direct" and "indirect"

methods.


Direct Methods

The essence of the direct method (as described by Knetsch and Davis [17])

is to ask a sample of recreationists how much they would be willing to pay

for their use of a facility rather than do without it. The problem with this

approach is in its application. Hypothetical questions tend to elicit hypo-









thetical answers, based on the respondent's own possibly prejudiced assump-

tions. A respondent may overstate his willingness to pay if, for example,

he thinks he might thereby promote improvement or duplication of favored facil-

ities. On the other hand, he might understate his willingness to pay if he

feared that his answer might be used to justify an increased facility use fee.

The inability to quantify such biases casts doubts on the accuracy of esti-

mates based on a direct approach, even though the aim of the approach is

theoretically sound. For that reason, the authors chose an indirect approach.

Indirect Methods

Indirect methods involve the use of some surrogate, or proxy, for facility

price. More precisely, the recreationist's willingness to pay is based on

observations of costs actually incurred in order to recreate at a facility.

Hotelling [13] is credited with the original ideal of using travel cost (the

cost of overcoming distance between the facility and a series of more or less

concentric distance zones around the facility) as a proxy for the price of a

visit to the facility, although Clawson [4] provided the first application of

Hotelling's idea. Later variations and refinements on the Hotelling-Clawson

approach include Brown et al. [2], Clawson and Knetsch [5], Burt and Brewer

[3], and Pearse [21].
Another group of writers, exemplified by Gibbs [9] and Edwards et al.

[6], divide total trip costs into travel costs, i.e., all costs incurred

while en route to and from the facility, and daily on-site cost, i.e., the

cost per day incurred while actually recreating at the facility. These two

components are then expressed as separate explanatory variables, with on-site

cost being chosen as the facility price proxy.

Gibbs' model contains a novel procedure for empirically delimiting the




5



feasible range of his equation explaining days per visit as a function of the

on-site cost. The idea is that there exist some upper limits to, or "critical"

values of, those costs above which the demand curve ceases to exist, and that

the limits would be reached at some finite quantity demanded. Specifically,

Gibbs hypothesized that (1) the critical travel cost is ceteris paribus, dir-

ectly related to the recreationist's actual on-site cost; and (2) the critical

on-site cost is directly related to the actual travel cost. For the single-

destination recreationist with which previous studies have been virtually ex-

clusively concerned, such hypotheses seem plausible, and have been supported

by Gibb's [9] empirical evidence. For multiple-destination recreationists,

the critical costs may be more strongly related to actual costs of visiting

other facilities on those people's itineraries. An easier way to obtain the

critical costs, and one that does not rest upon such hypotheses, is to find

out the minimum amount of time the recreationist would be willing to recreate

at the facility, and then to read from the demand estimate the value of the

price proxy that corresponds to that minimum amount of recreation. Examples

of this approach include Gibbs and Conner [10], and McGuire [183.

The model developed for purposes of the present study borrows more from

the Gibbs-Edwards type of approach than from the Hotelling-Clawson approach,

for several reasons. First, as Clawson admitted, total trip costs represent

the price of a "total recreation experience" [5, p. 33], which includes not

only recreation at a given facility, but additional enjoyments as may accrue

frum travel and reflection on the sojourn, before and after its undertaking.

Travel cost does not measure the value of recreation at the facility per se.

Second, the Hotelling-Clawson approach is essentially empirical, as pointed

out by Edwards et al. It relies heavily upon the tendency of large aggregates









to exhibit more uniform behavior with respect to a given influence, viz.,

average travel cost from given distance zones, than may smaller subsets of

those aggregates. By dealing with such large populations of people as exist

within a given zone, the influence of other important variables of demand may

be largely averaged out of the picture. Third, the on-site cost is a more

natural proxy for a facility's own price, which is, itself, a part of on-

site cost, while travel cost is wholely off-site cost.

Finally, in contrast to the Hotelling-Clawson focus on visits as the

quantity unit, the Gibbs-Edwards approach uses visitor-days actually spent

at the site (per visit and per time period) as the recreation quantity var-

iable. This visitor-day represents a more homogeneous recreation quantity

unit than either the Clawsonian visit (which does not take into account dif-

ferences among visitors' lengths of stay), or visitor-days, including travel

time (which ignores obvious differences between time spent traveling and time

spent at a facility). Visitor-days per time period on site of a facility

constitute a more integral measure of facility use intensity, the type of

measure of greatest relevance to recreation facility planning and management.

This visitor day is also the conventional product unit on which facility use

fees (the facility's own price) are levied.

It is not implied that the Hotelling-Clawson approach could not be modified

to account for differences in length of stay, but only that this has not been

done by previous users of the approach. More serious problems related to the

use of travel cost as a recreation price proxy,are explained more fully in

the following section.

Whatever their differences, a major common feature of all the indirect

approaches is their implicit assumption that the price of using a recreational









facility can be reasonably well represented by the costs of certain goods and

services that are purchased in conjunction with facility use. An implied

corollary is that the recreationists would react to a change in facility use

fee in the same way as they would react to an equal change in those ancillary

costs. This assumption is subject to both theoretical and empiricaldebate,

which is singularly scarce in previous literature.

Another similarity between previous studies is the absence of suggestions

of how to deal with the multiple-destination recreationist that is, the rec-

reationsist who visits other sites in addition to the given facility on a

single trip. Travel cost, which explains so much of the individual recrea-

tionist's demand for a single-destination facility, cannot be relied upon to

explain the demand for a facility visited on an itinerary that includes other

facilities. Since the aggregate demand for many common types of facilities

is substantially composed of multiple-destination visitors, there is clearly

a need for including them in a general theory of demand for particular recrea-

tion sites.

The role of leisure-time constraints on recreation demand is a topic that

has drawn considerable expression of concern, but little in the way of practi-

cal suggestions of what to do about them. Some theorizing has been done, for

example by Wilson [23], who conceptualizes outdoor recreation as a consumer-

produced good, and draws the arguable conclusion that the search for a facility

price proxy is irrelevant.


The General Theoretical Model


A theoretical model was developed out of the above historical context

and with regard to the basic elements of consumer demand analysis.








In general, an individual consumer's demand for a good can be expressed

as an equation relating quantity demand, Ds (measured as usage per time period),
to the good's own price, U (the facility's own price), a set of prices of rele-

vant substitutes and complements, P consumer disposable income, I, and a set

of utility variables, or preference-map shifters, T. The recreationist's usage

per time period is the product of two decisions; one of how frequently to visit
the facility, and the other of how long to stay per visit. A complete theory

of recreation demand should explain both frequency of visits, V, and length of

stay, Dv, resulting in two structural equations and an identify as follows:

(1) Dv = Dv(U, Pr' I, T)

(2) V = V (U, Pr' T)

(3) Ds = V D

Choice of a Proxy for Facility Price

In theorizing about proxy prices to represent variation in the nearly

invariant U, the logical place to seek such proxies is in the set, Pr, of

related prices. In past studies either travel cost, Et, ancillary on-site
cost, As, or both, have been used as facility price proxies. Travel cost
includes all costs incurred while en route to and from the facility, and an-

cillary on-site cost includes all costs incurred while actually on site of

the facility, net of the use fee (facility's own price), U. Separating out

these presumed related prices from the set Pr gives the model:

(4) Dv = Dr(U, As, Et, Px, I, )

(5) V = V(U, A,, Et, Px I, T),









where the variable set, Px, contains all the remaining prices of Pr, after

taking out the prices, A and Et. It should be noted that U, As and Et ex-

haust all the out-of-pocket trip costs of the recreationist.

The Inappropriateness of Travel Cost as the Proxy

As previously stated, As was chosen over Et as the source of proxy var-

iation in U. The reasons are as follows: First, both U and As are on-site

costs and already expressed in the same units, viz., dollars per day on site.

Travel cost per visitor day on site (Et/D ) would be inversely dependent upon

the length of stay, which is one of the dependent variables. Even where

quantity discounts (lower daily use fees for more days per visit) may be

granted, there is no such strong reason for doubting that Dv depends more

upon As than vice versa. The U (use fee) under consideration is not an entry

fee, but a payment which is based on a standard unit of recreation time.

Travel cost, like entry fees and other purely access costs, resembles a fixed

cost of the opportunity to do any amount of recreating at the facility.
The resemblance of travel cost to a fixed cost has been strongly con-

firmed by previous empirical research which has repeatedly found that, while

both the number of visits and length of stay are inversely related to As,

V is inversely related to Et (see, for example, [9, 10, and 18]). Thus,

as in the theory of production and cost, the magnitude of the fixed cost,

Et, determines the scale of the individual's recreational enterprise (view-

ing recreation as partly a consumer-produced good). Other things being

equal, the typical recreationist will stay as many days per visit as are

necessary to bring his average fixed travel cost per day on site of the given

facility down to an acceptable level.









The price of travel is an important explanatory variable, even if it is

not an appropriate facility price proxy. A problem arises here, however,

with the multiple-destination patron. In theory it is the marginal travel

cost of visiting the given facility to which he should be sensitive. Mar-

ginal travel cost may range from Et for the single-destination visitor to

nearly zero for the recreationist who views the given facility as merely a

convenient rest stop en route to elsewhere. The portion of total travel cost

that should be counted as a marginal cost of recreating at a particular facil-

ity is clearly related to the relative importance of that facility among all

other destinations of the trip. For this reason, a new technique has been

developed for the present study a travel cost adjuster.

Let r be the travel cost adjuster, Ms the subjective importance of rec-

reation at the given facility, and Mo the subjective importance of other rec-

reation received from the trip. Then r is hypothesized to be given by a

function such as:
Ms
(6) r M M
s Mo

Thus it is hypothesized that the relevant marginal travel cost of traveling

to a particular facility is given by rEt. A version of this hypothesis,

with tentatively suggested proxies for Ms and M is tested in a later sec-

tion of this bulletin.

Composite Prices, Ideal Proxies, Site Specificity, and On-Site Cost


Certain assumptions are necessary to justify use of the ancillary on-

site cost as the facility price proxy. Ancillary on-site cost is, in fact,

a composite price of a variable quantity mix of physical goods consumed.









The prices of those goods can be reasonably assumed given to the individual

recreationist, which is to say that he has no monopsony power over their de-

termination. The quantities, however, are functions of the prices, consumer

income, and the parameters of consumer preferences, or utility functions.

Having decided that As is indeed a price, there remains the task of

deciding whether it is an appropriate proxy for facility price. If one price

is an ideal proxy for another, then, in technical terms, the true coefficeints

of the facility price and the proxy price must be equal. The buyer would then

be behaving as if he conceptualized the price of a day's recreation as equal

to the sum, As + U. Prices of goods that are perfect complements would meet

these criteria. A less stringent condition is that the goods be equally site-

specific, though not necessarily purchased in rigidly fixed proportions. The

concept of site specificity is the crucial key to deciding the extent to which

the ancillary prices are, in fact, adequate proxies for the facility prices.

The cost of the angler's daily bait and tackle consumption could, for

example, be an ideal proxy for the facility price of a given site, but only

if there were no alternative places at which to fish. On that assumption,

a dol;lar-per-day change in the average daily cost of bait and tackle would

change the rational consumer's quantity of site use as much as would a dollar-

per-day change in the daily site-use fee. Both prices are perfectly, hence

equally, site-specific to unique facilities.

The assumption that the ancillary inputs bought with As are perfectly

specific to a given site is generally arguable. It takes only one alterna-

tive place for fishing to make the daily bait and tackle cost less than per-

fectly specific to the given site. In general, the less site-specific the cost,

the more its increase is reflected in the cost of recreating at all sites;

hence, the less the incentive to reduce use of, and/or abandon, the given









facility. The more site-specific the cost, the greater its increase pro-

vides incentive to seek out less expensive alternatives. It follows that,

other things being equal, the critical value of an on-site cost component

(U or As) would be inversely related, while the elasticity of demand with

respect to the component would be directly related to the specificity of the

component to the given facility.

One point must be clear: site-specificity is an issue only in a compar-

ative sense. If As and U are equally site-specific, which is the same as

equally non-site-specific, then there is no problem with the rational con-

sumer whose demand will be equally elastic with respect to a given change

in the use fee and in ancillary cost. Thus, for non-unique facilities, As

may still be a good proxy for U if the market happens to be characterized by

a form of price competition designed to maintain the relative market shares

of all competing enterprises. Pure competition would give this result, al-

though time would have to be allowed for expansion or contraction of indus-

try capacity before a predicted equilibrium would be established. Perfect

oligopolistic price leadership would be an equally suitable and more quickly

responsive type of market situation for assuming As a good proxy for U, on

condition, of course, that the given facility is one capable of exercising

the price leadership. In either type of market structure, the key lies in

maintaining ratios between prices of all substitutable facilities. The greater

the extent to which everyone's use fees vary in tandem, the less specific is


Other on-site costs, for example food, may better reflect the cost of
subsistence, rather than recreation per se. While netting out subsistence
costs is a serious empirical problem it need not be a theoretical one. Thus,
for purposes of this theoretical discussion, A may be assumed to contain
no subsistence costs.










a given facility's price to itself.

Some degree of uniqueness or local prominence among competing facilities

is not atypical of many public outdoor recreation sites. In the cases of

facilities such as federal and state parks, their existences can generally

be attributed to the public sector's unique ability to conserve large por-

tions of unusual natural environments and maintain a monopoly over them. The

public facilities may also exercise a degree of unconscious price leadership

over such establishments as, for example, commercial campgrounds, whose own
existences may be due largely to the public parks. Thus, the assumption that

the use fee, U, and ancillary cost, As, are about equally, though imperfectly,

site-specific may be appropriate for such facilities.

The Conceptual Model, with On-Site Cost the Choice of Proxy

With the caveats stated, the theoretical model developed in the fore-

going consists of the following equations:


(7) Dv = Dv(Es, rEt, I, Px, T)

(8) V = V(Es, rEt, I, Px, T)

(9) Ds = V Dv
for E < E*

The variable, E = U + A has been selected as the market equivalent facil-

ity price proxy. The model is specified subject to the restriction that Es

cannot exceed the critical E*. All other variables are as previously defined.

Discussion of the remaining variables, I and the components of the sets Px

and T (in which perhaps a time constraint should be included), is contained
in a following section.









Equations (1) and (;2) are not a simultaneous system in the econometric

sense if all right-hand variables can be assumed exogenous, which is deemed

reasonable in view of the data base described in a subsequent section. At

the same time, it is difficult to conceive of an independent variable belong-

ing to either Equation (1) or (2) that does not also enter the other. In

this sense, estimation of the two relationships separately will provide in-

formation concerning the relationship between length of stay and visiting

frequency.

Readers of Oliveira and Rausser [20] may be tempted to view Equations

(1) and (2) as reduced forms of simultaneous user demand and supply equa-

tions, inasmuch as the independent variables may include some that reflect

conditions of supply (in particular, quality of supply) as well as demand.

The basic "demand" nature of the equations can be argued on two grounds:

First, that quantity supplied of tangible use potential is essentially immune

to effects of variation in any of the conceivable independent variables, and

second, that the typical state park camper encounters less than fully-occupied

campgrounds, making usage almost totally a question of demand.

Sample Data


The theoretical model, as with any conceptual framework, needs empirical

data to test its applicability. While the main focus of this bulletin is the

development of a defensible theoretical model to describe recreationists'

demand for recreational facilities, it is appropriate to include a discussion

of the empirical counterpart.

The problem was to obtain a representative sample of data from a large

study area at reasonable cost in time and money. It was discovered that state










park registration files contain names and addresses of past campers, which

raised the possibility of a telephone survey of those campers as perhaps a

justifiable way to cover a statewide system of facilities. Camping at Florida

state parks forms the data base for applying this theoretical model. While

the results are representative of the state park system in Florida, the gen-

eral implications and applicability of the model are valid for many areas.

A telephone survey was adjudged the most efficient way for purposes of this

study.

A sample of campers visiting Florida state parks between April 1972 and

July 1973 was drawn. The 36 parks with campgrounds were first stratified by

location--those north and south of Orlando, Florida.. A representative sample

of 10 parks was chosen while maintaining a balance within important geograph-

ical differences (including seaside versus inland parks). The 10 sample parks

accounted for 63 percent of total state parks registrations in fiscal year

1973. Available campsite occupancy data [8] suggested that an acceptable

sampling precision could be obtained from completed interviews with about

400 visitors divided equally between the northern and southern sample parks.

That target sample was allocated among the sample parks according to porpor-

tional use received. Within each park the sample to be surveyed was distributed

between a high and a low use season, again based on proportionality. Of the

slightly over 800 names and addresses of campers obtained from the sample

park registration cards, the telephone survey produced 357 completed inter-

views, or 89 percent of the 400 interviews targeted. Those completed inter-

views comprise .064 percent of total 1973 registrations at the ten sample

parks and .020 percent of total 1973 registrations (including renewals) at

all state parks with camping. More details of the sampling procedure and

questionnaire can be seen in [15].









THE STATISTICAL MODELS


The statistical counterpart of the theoretical model consists of the

following equations:

(10) In Dv = In a10 + a1 In Es + al2 rEt In Es + al3 In (rEt)

+ a14 In I + a15 In (1/N) + b11 S + b12 D + b13 X


(11) In V = In a20 + a21 In Es + a22 rEt In Es + a23 In (rEt)

+ a24 In I + a25 In (1/N) + b21 S + b22 D + b23 X


(12) In Ds = In V + In Dv

for Es < E *.

Definition of Variables


The a.. and b,. are the structural parameters to be estimated. The

variables are defined as follows:
Dv = length of stay per visit by the recreation group in 12-hour periods.

V = visits per month by the recreation group to a park in the universe
sampled during a given season (summer or winter).

Ds = use per month in 12-hour periods (Ds = V 6 Dv).

Es = on-site cost per recreation group, in dollars per 12-hour period
(Es = U + As).

rEt = adjusted round-trip travel cost per group, where:
Et = total travel cost, including all transportation, lodging,
and other out-of-pocket expense from home or other point
of origin and back to origin, net of costs incurred while
actually present on site of the given facility.

r = travel-cost adjuster.










I = recreationist's family income before taxes.

N = number of persons in the recreation group.

S = a seasonal dummy, where low demand season = 0 and high demand
season = 1.

D = a major-destination camper dummy, where 1 = major destination
visitor and 0 = non-major destination visitor to the given parks.

X = a tent-camper dummy, where 1 = tent camper and 0 = recreational-
vehicle camper.

E* = the critical, or maximum, on-site cost the recreationist would
s be willing to pay per group rather than not visit the site at all.

Some of the above variables deserve more detailed explanation. Frequency

of visits is expressed on a monthly basis because of the presence of the sea-

sonal dummy, S, and because the seasons as defined are of unequal length.

The case where S = 1 refers to the season in which rate of use, Ds, is above

the yearly average for the given group of parks. Table 1 explains the divi-

sion of seasons. Separate estimates of the model were made for parks north

and south of Orlando.

The travel-cost adjuster, r, is estimated by:


(13) r = (T1 + Dv)/T2'

where T1 is the total necessary round-trip travel time (directly to the site

and back home, at reasonable speed), and T2 is the total time actually away

from home. Thus, time is used to measure the relative importance specified

in the theoretical travel-cost adjuster, Equation (6). This admittedly ar-

bitrary adjustment is deemed less arbitrary than using total unadjusted travel

cost in explaining demand for sites that serve multiple-destination recrea-

tionists. Actual time, T2, was determined with the questionnaire. Total ,

necessary time was estimated on the basis of map sources ([1], [8], [22]),










and the authors' own travel experiences.


Table 1.--Breakdown of seasons


Area High season Low season


North...................April-August (5 mo.) September-March (7 mo.)
South...................December-April (5 mo.) May-November (7 mo.)


SOURCE: Data from Florida Department of Natural Resources.

Personal income before taxes was the measure of income used in the model.

A better estimate of actual purchasing power would have been disposable in-

come (excluding income taxes), but it was thought that a typical interviewee

would be more aware of his family's before-tax income than of how much income

taxes were paid. In view of the complexities of federal, state, and local

income tax codes, no attempt was made to derive disposable income from per-

sonal income.

The seasonal shifter, S, is a catch-all dummy for all seasonally induced

reactions by both sellers and buyers of Florida recreation. It is a utility

variable and also a price-of-alternatives variables, since seasonal price

discrimination is a highly profitable and widely practiced art of private

enterprise, as a perusal of any major hotel's rate schedule illustrates (see,

for example, [14]). Since commercial campgrounds are a fast-growing sideline

of nearly all the major hotel chains in Florida, the seasonal price-of-alter-

natives component of S can be expected to increase in the future.

The variables N, D, and X are also surrogates for utility parameters.

The tent-camper dummy, X, also may capture some of the influence of the value

of durable recreation equipment on quantity of site use. Its hypothesized









coefficient would be negative. For equally obvious reasons, the hypothesized

coefficient of D would be positive. Group size N is included primarily to

account for variation in campers' characteristics.

Choice of Equation Form


Past experience in the estimation of outdoor recreation demand suggests

that the relationships are curvilinear. The simplest types of curvilinear

equations to estimate are logarithmic forms and, in fact, logarithmic forms
2
have performed well in previous empirical studies.2

The algebraic equation form chosen is a modified constant-elasticity-

of-demand (CED), or exponential, function. The basic CED function was modi-

fied in order to test a version of Marshall's [19, p. 8] principle of lower

elasticity of demand for items less important in the consumer's budget; that

is, the hypothesis that the elasticity of facility use, with respect to the

facility price proxy, is inversely related to his adjusted travel cost. That

modification is as follows:
bI + d t c2 c3
(14) Dv = cE (rEt) I

which is linear in logarithms. According to Marshall's principal, dI > 0,

since bI < 0 if Es is a good proxy price and Dv is a normal (not inferior)



2According to the mathematics of the neoclassical theory of consumption
and demand, the demand of the rational consumer is homogeneous of degree zero
in prices and income. (For a relatively simple modern interpretation, see
Henderson and Quandt [11, Ch. 2].) Only a curvilinear equation could fulfil.
that condition. The modified CED equation is capable of degree-zero homo-
geneity, but does not force it. A strictly linear demand equation cannot
be homogeneous of degree zero.










good. By definition, the Es elasticity of Dv is given by bI + d1rEt, and

similarly for the Es elasticities of V and Ds.

An alternative model, substituting costs per person, Es/N and rEt/N,

for the per-group costs, Es and rEt, was also estimated for each of the two

Florida sub-regions. The estimates are not shown in this bulletin, but are

given in [15].

It makes negligible difference to the equation estimates whether costs

per group or costs per person are specified. Where, as in the present case,

the use fee is levied on a per-group basis, it is somewhat more convenient

to express the on-site and travel cost on the same basis. At any rate, no

more reasonable criterion is apparent.










THE ESTIMATED MODELS


Estimates of the D and V relationships are shown in Tables 2 and 3,

respectively. The variables are defined as before. Standard errors of the

coefficient estimates are shown in parentheses under the estimates. All

equations were estimated by the method of ordinary least squares.

For each estimated equation, the residuals were examined for non-sper-

ical disturbances. In general, the assumption of random errors seems tenable.

There is some evidence of heteroskedasticity in estimates of the visits re-

lationship, suggesting a geometrically positive correlation between the error

term and frequency of visits. There was no attempt to correct for this since

(1) the problem seemed minor among more obvious problems with the visits

equations, and (2) a vast majority of observations fall in a small range of

visits within which homoskedasticity can be reasonably assumed. Correlation

matrixes of the variables are included in the Statistical Appendix.


Length-of- stay Equations

The interaction terms, while statistically significant for the northern

parks, show up with a negative coefficient estimate for D which is con-

trary to the hypothesized lower elasticity of Es demand at greater adjusted

travel cost. For southern parks the interaction term was not significant.

However, the statistical characteristics of the estimates are encouragingly

congruent with theoretically based expectations.

From a statistical standpoint, the travel-cost adjuster renders notable

improvement in the Dv equation estimates. A comparison between the results

of specifying total (unadjusted) Et instead of rEt is shown in [16]. In








Table 2.--Coefficient estimates of the length-of-stay (Dy) relationship: Florida state parks, 1973

constant(
Equation term In E In (rE) rEt In E

-----------------------------------Northern parks------------------
(15) -2.337 -4.34*** .629*** -.00016***
(.074) (.046) (.00004)
---------------------------------- Southern parks---------------------
(16) .508 -.518*** .577*** .00020
(.087) (.071) (.00013)

Degree of 2
Equation In I In(/N) S D X Subject to freedom F R
-------------------------------------------Northern parks---------------------------------
(15) .183*** .155*** .166*** .726*** -.092 E < 18.82 168 49.447 .702***
(.068) (.077) (.071 (.073) (.074) s

----------------------------------------Southern parks---------------------------------
(16) -.093 -.069 .057 .598*** -.215*** E < 21.57 171 32.600 .604***
(.066) (.096) (.086) (.091) (.085) s


Significant at 10 percent level.
** Significant at 5 percent level.
*** Significant at 1 percent level.


SOURCE: Sample data.







Table 3.--Coeff-cient estimates of the frequency-of-visits (V) relationship with adjusted travel cost:
Florida state parks, 1973

Constant
Equation term In Es n (rEt) rEt n E

-----------------------------------Northern parks-------------------------
(17) -1.015 .094 -.335*** .00027***
(.112 (.069) (.00006)
----------------------------------Southern parks-------------------------
(18) -1.801 -.017 -.084 -.00001
(.069) (.057) (.00010)


Degrees of 2
Equation In I In (1/N) S D X freedom F R
-------------------------------------Northern parks--------------------------------
(17) .029 -.061 .387*** .459*** .023 168 6.883 .247***
(.103) (.116) (.107) (.109) (.111)
-----------------------------------Southern parks------------ --------------------
(18) .048 .037 .124* .290*** -.083 171 3.497 .141***
(.052) (.076) (.068) (.072) (.068)


*Signifivant at
**Significant at
***Significant at


10 percent level.
5 percent level.
1 percent level.


SOURCE: Sample data.









every case, use of adjusted travel cost results in a greater number of sta-

tistically significant parameter estimates as well as a notable improvement

in the coefficient of determination.

The critical costs in the "Subject to" column of Table 2 are inferences

from the estimated length-of-stay equations. The critical cost corresponds

to that value of on-site cost obtained by substitution of the average inter-

viewee's declared minimum acceptable length of stay needed to justify the

time and expense of the visit, in the manner of [10] and [18]. At the crit-

ical cost the recreationist would take only his minimum acceptable length of

stay, and at higher on-site cost would not visit at all.

Frequency-of-Visits Equations


It is more difficult to summon enthusiasm for the visits equation esti-

mates in Table 3, although the F-values are high enough to suggest that the

problem may be more incompleteness than otherwise erroneous specification.

There is some evidence, however, that a part of the problem may be the need

for a better procedure to account for travel cost.
In contrast to the case with the Dv equations, the statistical charac-

teristics of the V equations using adjusted travel cost are not notably dif-

ferent from the result of substituting total travel cost for rEt. Indeed,

making that substitution, the coefficients of Et become significant at the

1 percent level for the southern parks, while the coefficients of rEt are

not statistically significant for those parks. (These comparisons may also

be seen in [15].) That this may not be due to random happenstance is sug-

gested by both a point of theory and an empircal fact.

The theoretical point is the concept of marginal travel cost as an al-










ternative cost of other desirable (and available) destinations foregone. In

this sense, the marginal travel cost of visiting a particular facility con-

sists of the benefits, or value, that could have been obtained by recreating

elsewhere instead of at the given facility. Logically, this poses the seem-

ingly formidable practical problem of accounting for the value of all next-

most-valuable recreational alternatives to trips within the vicinity of the

particular facilities under study.

The empirical fact is that the visitor to a southern park paid over twice

the travel cost of the visitor to a northern park, and came from over twice

as far away. This was not due solely to the length of the Florida Peninsula,

since the northern parks received a considerably higher percentage of in-

state and border-state visitors than did the southern parks. It is reasonable

to assume that the numbers and variability of alternatives considered by a

group of recreationists would, other things being equal, be directly related

to the distance (or, as suggested by the geometry of circles, the square of

the distance) between their points of origin and the particular facilities.

In other words, the greater the distance traveled, the more the travel cost

measures the influence of alternative forms of recreation foregone.

If higher total travel cost implies the consideration of greater numbers

of higher-valued substitutes for use of particular facilities, then the elas-

ticity of visits with respect to travel cost is perhaps not constant, but

increasing. Two alternative equation forms (the strictly linear and the power-

of-e function), do give an increasing Et elasticity; however, both gave less,

rather than more, statistical confidence in the estimated influence of Et on

V. Those results, of course, by no means reject the hypothesis of increasing

Et elasticity of visiting frequency. The only conclusion to be drawn at this










point is that visiting frequency needs a better conceptualization. The

Hotelling-Clawson method of using average costs of traveling from given dis-

tance zones glosses over this problem as does any attempt to estimate a func-

tion on the basis of averages instead of the highly (and only perhaps random-

ly) variable observations from which the averages are computed. In statis-

tical analysis, the computation of average variables for use in a regression

analysis may constitute an evasion of the hard task of improving economic

theory.

Had total usage, DS, been regressed on the independent variables speci-

fied in this study's models, the numerical values of the coefficient esti-

mates would necessarily have been the same as the results of combining the

Dv and V estimates through the identity Ds = V Dv. It was verified that

fairly good statistical characteristics of the Ds equation are achieved by

such an approach, as can also be seen in [6]. The decomposition of Ds into

its components, D and V, thus aids the refinement of theory by pointing out

a trouble spot. Unreliable estimates of the V relationship undermine confi-

dence in statistically "reliable" estimates of the Ds relationship.

A Note on Leisure Time Constraints


The authors made two attempts to estimate the influence of a leisure

time constraint, both attempts being based on the answers of respondents to

the following question: "Why do you not camp more in these state parks?"

Is it mainly the cost of travel, etc., of recreating there, or is it mainly

the lack of time for taking such excursions?"

Of the 357 respondents in the sample, 279, or 78 percent, gave money

cost as the primary constraint of their recreation at the given type of facil-










ty. Thirty-five, or just under 10 percent, cited limited time as their more

effective constraint. The remainder could not make up their minds.

A dummy variable was used in the statistical model to distinguish campers

who cited time from those who cited cost as the contraint on their activity.

No statistical significance attached to that dummy's coefficient. A dummy

was then included to distinguish between weekend campers and all other campers.

That dummy also was not significant statistically.

The fact that such an overwhelming majority of respondents cited cost

instead of time as their constraint suggests that omission of explicit time

variables does not seriously harm empirical models of demand for facilities

such as the Florida state parks;









INFERENCES FROM THE ESTIMATED MODELS


The estimated models constitute explanations of the typical recreation-

ist's behavior with respect to the independent variables. The purpose of

this section is to highlight characteristics of that behavior which may be

relevant to facility planning and management, and to illustrate how the models

can be used in formulating planning and policy criteria based on some of those

characteristics.

Use as a Function of Travel Cost


The estimates confirm the findings of previous studies that higher

travel cost, while reducing visiting frequency, increases length of stay per

visit. Moreover, the positive influence of adjusted travel cost on length

of stay prevails over the negative influence on visiting frequency, making

travel cost a net positive influence on use per time period, Ds. This can

be seen by inspection of Equations (15) through (18) (Tables 2 and 3).

In general, the form of the equation giving Ds as a function of rEt,

ceteris paribus, is:

(19) In Ds = a + b In (rEt) + c (rEt In Es),

where a is a constant resulting from holding all other variables at their

appropriate mean values, and b and c, are the sum of the estimated coeffi-
cients of adjusted travel cost and interaction term, respectively, from the

V and Dv equations of each model. The elasticity of Ds with respect to rEt

is given by the derivative:

(20) (ln Ds)
(20) rIn t = b + c rEt In E.
a In (rEt)t s









For equations (16) and (18) (the model for northern parks), b = .629 .355 =

.294, and c = -.00016 + .00027 = .00009. Substituting these values and the

mean value of the interaction terms into Equation (19) gives .294 + .00009

(328.99) = .590.3 Doing likewise for Equations (16) and (18) gives, in

summary:

Northern Parks:

(21) (In Ds
in (rE t = .294 + .0009 (328.99) = .590.

Southern Parks:

(22) (ln Ds)
In (rE = .493 + .00019 (391.56) = .567.

Both evaluations are positive. Thus according to the estimates, the typical

Florida State park camper makes greater use of the parks, the larger his

adjusted travel cost. He visits less frequently than the average recreation-

ist, but stays so much longer per visit that his total use is greater than
average. This is consistent with the concept of travel cost as overhead.

An implication is that thetypical major-destination visitor from out-of-state



3The arithmetic mean of the logarithm of a variable, X, corresponds to
the geometric mean of X, i.e.:

-I N N
In (1/N) Z In X. = ( X.) 1/N
i=l i=1
The regression hyperplane passes through the arithmetic means of In V, In
D In E In (rE ), In I, and In N. The exponential form of the equations
tKus passes through the geometric means of those variables. Thus, the term
"average", as used herein for deriving predictive equations of response to
particular variables, always refers to the geometric mean of a variable
transformed into lojaritlhms. The arithmetic mean is the appropriate average
for the dummy variables only, which are not transformed into logarithms.
The interaction term is a hybrid of transformed and untransformed variables.
The regression hyperplane passes through the arithmetic mean of rE In E ,
for example, which the regression program treats as a separate variable.









uses the parks more than the typical in-state camper.

Use as a Function of On-Site Cost


The variable Es, on-site cost, includes and is the proxy for the use fee,

U, and constitutes the only variable under the direct control of park manage-

ment. Thus, the possibilities of influencing use by variation of U, hence

of Es, are of special interest.

The Equations
Relationships showing facility use, Ds, as a function, ceteris paribus,

of on-site costs, are derived by holding all other independent variables at
their appropriate mean values. The results of doing this for Equations (15)

and (17) and (16) and (18), are Equations (23) through (28), respectively:

Northern Parks:

(23) In Dv = 2.614 .458 In Es;

(24) In V = -1.633 + .135 In Es;

(25) In Ds = In (V Dv) = .981 .323 In Es.

Southern Parks:

(26) In Dv = 2.801 .480 In Es;

(27) In V = -1.573 .019 In Es;

(28) In Ds = In (V Dv) = 1.288 .499 In E .

The differences between the coefficients of In Es for Equations (15) through









(18) and (23) through (28) arise from the repeated presence of In Es in the

interaction term.

On-site cost was found to be a statistically significant variable in the

equations explaining length of stay, Dv but not significant in the equations

explaining frequency of visits, V. In the V relationship, Equation (24), the

positive Es elasticity even contradicts theoretical expectation. This points

out one of the advantages of estimating the visits and length-of-stay rela-

tionships separately. Anyone using the estimates is thereby apprised of the

possibility that a portion of the recreationist's total use may be unreliably

explained, viz., that portion which estimates the effects of Es upon V in the

present instance. That fact could not be known were only the Ds relationship

estimated directly, even though the coefficient estimates of the estimated

Ds equation would be the same as those of the derived Ds equation. Indeed,

it was verified that the Es elasticity estimate is significant at the I percent

level in all estimated Ds relationships, a finding which the present procedure

reveals as possibly misleading.

There are two lines of argument on the question of how to proceed with

use of the estimates from this point. On the one hand, there is a theoretical

argument for having the variable, Es, in the "visits" relationship despite

the failure to confirm its influence statistically, and since one of the goals

is to predict Ds, theoretical consistency might best be served by basing pre-

dictions on Equations (25) and (28'). On the other hand, since the empirical

results fail to confirm any influence of Es over V, the more empirically minded

may be disposed to assume that on-site cost has negligible influence upon

visiting frequency, and base all predictions of the effects of Es on manipu-

lation of the length-of-stay relationship. For present purposes, the predic-









tions will be based on the derived Ds relationships, Equations (25) and (28).

According to the elasticity estimates contained in those equations, a 10 per-

cent increase in daily on-site cost would reduce the average recreationist's

total usage by around 3.2 percent at northern parks and 5 percent at southern

parks. These predictions are also, of course, subject to the assumption of

equal site specificity of U and Es, as previously explained.

Another type of prediction that can be based on the Es-elasticity is of

how the average recreationist's contribution to fee revenues may vary with

the use fee. To give an idea of the magnitudes involved, the predicted re-

sults of a hypothetical 50-cents-per-day fee increase are calculated and

shown in Table 4, for the actual sample data. Column (5) contains the pre-

dicted declines in total usage per month. Thus, the predicted effect of a

50-cent increase in on-site cost per 12-hour period would be to reduce the

average northern park visitor's monthly use by .04 12-hour periods, or .48

12-hour periods per year. For the same increase in daily group on-site cost,

the average visitor to a southern park would reduce his recreation by an esti-

mated .06 12-hour periods per month, or .72 12-hour periods per year. The

current use fee is approximately $2 per recreationist group per 12-hour per-

iod at all state park campgrounds; thus, the current fee burden is $4.44

(= $2 2.22 periods) per month at the sample northern parks and $4.36

(= $2 2.18 periods) per month at the sample southern parks. Raising the

fee to $2.50 would reduce use per month to an estimated 2.18 (= 2.22 .04)

periods per month at northern parks and to 2.12 (= 2.18 .06) periods per

month at southern parks. Thus the predicted fee burdens would be (2.18)

($2.50) = $5.45, and (2.12)($2.50) $5.30 per group per month at northern

and southern parks, respectively. In summary, the predicted effects of the







Table 4.--Prediction of the change in usage per visitor-group due to a 50-cent increase in group daily
on-site cost

Percentage
equivalent
Arithmetic average of a 50-cent Arithmetic average
Estimate on-site cost per increase in usage for sample Predicted change in
group for sample daily on-site (12-hour periods usage (12 hour
($ per 12 hours) cost per month) periods per month)
(1) (2) (3) (4) (5)
North.......... 9.66 5.2 2.22 -.037

South.......... 8.62 5.8 2.18 -.063


SOURCE: Sample data.









50-cent increase would increase the fee burden per northern recreationist

group by $1.11 per month, and per southern recreationist group by $0.94 per

month.


Implications for Aggregate Demand

These models, being explanations of the demand of the average, or "typ-

ical", consumer, contain no equation explaining the total number of recrea-

tionists who patronize the parks. Such an equation would have to explain

not only the behavior of the universe of actual patrons, but the behavior

of potential patrons as well. While it is beyond the scope of this study to

explain the behavior of potential patrons, a few words on the principles and

problems of relating individual to aggregate demand are appropriate.

It is reasonable to assume that some potential patrons are non-patrons

of the state parks because.the actual on-site cost would be above its criti-

cal value to them. Short of a sample survey of the population of North Amer-

ica, there is no feasible way to acquire information on the individual charac-

teristics of those potential patrons and their demands for use of the state

parks. In order to predict the number of new patrons that.would visit for

various hypothetical reductions of the user fee, it would be necessary to

know the numbers of potential patrons whose critical on-site costs fell within

a given range below the actual on-site costs of their use, were they to visit.

Some inferences about those numbers might be made based upon the relative

proportions of users in certain socio-economic classes of the population in

combination with separate estimates of the model and of critical costs for

subsamples of actual patrons, stratified according to socio-economic charac-

teristics. The size of sample needed for such a procedure would be quite

large.









Use as a Function of Seasonal Change

The influence of seasonal change on facility use is measured by the

estimated coefficient of the seasonal dummy variable, S. This variable was

statistically significant in all of the estimated V relationships, and in

both of the estimated D equations for the northern park visitor. It was

not significantly different from zero for the Dv equations of the southern

park visitor.

In terms of the Dv relationships as expressed in Equations (23) and (26),

for example, the effect of seasonal change is estimated as the difference in

the constant term as S is set equal to zero (for low-demand season) and then

equal to one (for high-demand season). For the northern parks visitor, the

resulting equations are as follows:


(29) In D = 2.504 .458 In Es (S = 0).

(30) In Dvl = 2.670 .458 In Es (S = 1).

From Equations (29) and (30), the relative difference in the estimated

average length of stay between seasons is calculated as follows:

(31) In Dvl In Dvo = 2.670 2.504 = .166,

D v/Dvo = e166
v1 vo

Dv1 = 1.18 Dvo.

Thus, the average summer visitor spends an estimated 18 percent longer per

visit than does the average winter visitor to the northern parks,

The absolute differences in seasonal length of stay given by Equations









(29) and (30) are between geometric means. To calculate the comparative

seasonal arithmetic mean lengths of stay from the equations, it is necessary

to assume that the relative seasonal differences between the arithmetic and

geometric mean lengths of stay would be approximately equal. On that assump-

tion, Dvo = 5.96 12-hour periods, and Dvl = 6.95 12-hour periods, as compared

to the arithmetic yearly average, Dv which, for the northern sample, is 6.56

12-hour periods. The difference is approximately 13 hours per visit between

the (arithmetic) average summer length of stay and the average winter length

of stay at the northern parks.

By the same method, and using the arithmetic sample averages reported

in the Statistical Appendix, estimates of seasonal variation in length of

stay, visiting frequency, and total use per visitor group were calculated

and are shown in Table 5. The much greater seasonal variation in use and its

components in northern parks is quite apparent.

Use per recreation group, Ds, is the part that the model explains of

aggregate use, which can be measured on the basis of campsite occupancy data

[8]. Assuming one campsite per visitor group, the last 3 rows of figures in

Table 5 represent what the model does not explain, namely, that an estimated

75 percent more people visited the northern parks during the summer season

than during the winter season, while twice as many visitors came to the south-

ern parks during the winter season as came during the low summer season.

Estimation of Recreation Value


A measure of value known as consumer surplus can be derived from the

demand estimates. While there are several alternative concepts of consumer

surplus [11, chap. X], for practical purposes it can be defined as an area








Table 5.--Estimated average and seasonal components of campground use,
Florida state park system, 1973

Use component estimate Northern parks Southern parks

Sample average length of stay per visit,
in 12-hour periods (D ):
Both seasons average (D ) ............ 6.56 8.63
High season estimate (Dvl)............ 6.95 8.32
Low season estimate (Dvo )............ 5.96 8.85

Sample average visits per month (V):
Both seasons average (V)............. .370 .232
High season estimate (V1)............. .424 .246
Low season estimate (V )............ .288 .218

Sample average use per recreation group,
in 12-hr. periods per month (D = V-D ):
Both season average (T ) ............. 2.43 2.00
High season estimate (Dsl)............ 2.95 2.00
Low season estimate (D o) ............ 1.72 1.93

Recreation groups per month in all
park: (G):
Both seasons average (G)............. 95 91
High season estimate (G1)............. 128 129
Low season estimate (G )............. 73 64

Aggregate use, all parks, in 12-hour
periods per month (G-D ) :
Both seal.oni average (GDs ) .......... 230 182
High season estimate (G IDsl)......... 378 264
Low season estimate (G Dso).......... 125 124


aFigures presented are arithmetic means and equivalents.
bSeasonal estimates are not statistically different from both seasons'
average .
cEstimate of recreation groups (G) is based on the assumption that each
group ouc~cjies one .ampisite.

SOURCE: Sample data and tabulation of Florida park attendance, Tallahassee,
1972 (mimeographed).









under the price-quantity demand curve. In Figure 1, for example, the consumer
surplus is equal to the area, Es a b s, where Es* is the'camper's critical

on-site cost, Es his actual average daily on-site cost, Dsm his minimum accept-

able use, and Ds actual average use. The reasoning behind this concept of

value is as follows: The camper would be willing to pay E* daily for the

first Dsm days of recreation, but, in fact, pays only Es daily for this same

amount, and, thus, earns a surplus value equal to the area E* a c E which

is the difference between the maximum money he would be willing to pay and

the actual money he pays for the minimum acceptable use. For additional days

he pays Es per day, but would be willing to pay more until he reaches equil-

ibrium at Point b, where he pays for the last moment of his use exactly what

it is worth to him. Thus, the area, abc, is also a part of his surplus, or

unpaid-for, value.

With reference to Figure 1, the mathematical expression for the average
recreationist's consumer surplus, CS, is as follows:

E*
(32) CS = s f(Es) dEs.

Es

The function f(Es) is one such as Equations (25) or (28).

Value Received from Northern Parks

The average northern park visitor's use as a function, ceteris paribus,

of Es is given by Equation (25). In its untransformed version, this equation

is written as follows:

(33) Ds e981 E-323


where: E* = $18.82; E = $8.50
S 5












Daily on-site costs (E )









*
E
s s a
I

















0s ___ I-------------------
E I b

I I

I D s D (Es)














D Use per time period (D)
a S
s


Figure 1. Illustration of consumer surplus









The critical on-site cost corresponds to the geometric mean minimum length

of stay. Average on-site cost is also the geometric mean. The corresponding

definite integral, with its evaluation, is:

i f$18.81 -.323
(34) Value per month per group = e981 Es dEs = $11.96.
$8.50


Dividing the value of Equation (34) by the geometric mean use per month (1.335)

gives an estimated value per 12-hour period of $8.95 per group. Since the

mean number of visits per month is .261, this is equivalent to a value of

$45.82 per visit of the average group ($11.96 .261).

The equivalent value per person, based on the geometric mean group size

of 3.64, is $12.59 per visit. Using the number of visitors for the fiscal

year 1972 (from Florida Department of Natural Resources [83, which was an

estimated 340,700 campers to the northern sample parks, the total value pro-

duced by the northern samples for campers in that year would be calculated as

approximately (340,700)($12.59), or somewhat more than $4,289,000. Assuming

the sample parks are representative of all northern parks, the estimated value

for the approximately 1,117,500 campers received from all parks north of Orlando

would be (1,117,500)($12.59), which rounds off to an estimated $14,000,000 for

the fiscal year 1972.

The effects of seasonal change are borne entirely by the seasonal dummy,

S. Thus, the effect of seasonal change on value per month is represented

entirely by varying the exponent of e in Equation (34). The exponent, .981,

results from setting S at its mean value, S = .661. When S = 0, the exponent

becomes .621; when S = 1, it is 1.16. The resulting value estimates are sum-

marized in Table 6, which is derived directly from Equation (34), as just des-









cribed by substitution of the appropriate value of S.


Table 6.--Estimated value of camping to the recreationist group: Florida
northern state parks

Value Value per Value
Time of aar per month 12 hours per visit

(1) (2) (3) (4)

Low season (S = 0)... $ 8.34 $ 6.25 $35.01

High season (S = 1).. 14.38 10.77 55.15

Total year (S = S)... 11.96 8.95 45.86


SOURCE: Sample data.


Since the Florida state park campsite fee is levied on a group-daily

basis, it is of interest to examine the estimated consumer surplus per day

of recreation on-site. Having used the same yearly geometric average costs

as the limits of integration in calculating both yearly and seasonal average

values, it is appropriate to use the yearly geometric mean length of stay

(= 5.122 12-hour periods) for calculation of both yearly and seasonal values

per recreation day. These estimates are shown in Column (3) of Table 6. The

seasonal difference between willingness to pay might be considered by policy

makers as a basis for seasonal fee discrimination. This is not to suggest

that public enterprises should price their services at what the traffic will

bear, or even at full cost of production, which would doubtless be politically

infeasible, not to mention ideologically repugnant to many of the people. It

is something quite different to suggest that, where greater than token fees

are charged, they be made to bear some relationship to the value of services

received. On that basis, it is noted that these models give estimated differ-










ences of approximately 53 percent between the value of a summer's day and a

winter's day of recreation at the northern parks.


Value Received from Southern Parks

The estimated relationship showing the southern per-visitor's use as a

function, ceteris aribus, of on-site cost is Equation (28) which, in its un-

transformed version, is written:

1.228 -.499
(35) Ds = e228 E-

where: E* = $21.57; E = $7.60.
5 s

The'corresponding value estimate per month thus becomes the definite integral:

1.28 4* 499
(36) Value per month per group = e228 $21.57 dE = $12.93.

$7.60

Dividing the value of Equation (36) by the geometric mean use per month (1.243

12-hour periods) gives an estimated value per 12-hour period of $10.40 per

group. The geometric mean number of visits per month is .200; thus, the value

per visit of the average group is estimated at $64.65 ($12.93 .200).

The value received per person, based on the geometric mean group size of

3.16, is $20.45 per visit. For the estimated 213,800 campers of fiscal year

1972, the total value produced by the southern parks for campers in that year

is calculated as approximately $4,372,000. Assuming the southern sample parks

are representative of all southern Florida state parks with campgrounds, the

total value of the latter to their estimated 706,400 campers was approximately

$14,446,000 in fiscal year 1972.

For low-season use (S = 0), the exponent of e in Equation (36) becomes









1.194; for high-season use it is 1.261. The resulting seasonal value estimates

are shown in Table 7. According to the estimates, value per group per month

ranges from $12.49 during the low-demand, or summer, season to $13.36 during

the high-demand, or winter, season in the southern parks. Value per 12-hour

period is estimated at $10.05 for low season and $10.75 for high season. That

seasonal differences in value are large in the north and small in the south

was expected in view of the comparative climatological characteristics of the

two regions. The estimated difference between the value per group per day is

also small, being around 7.5 percent higher for the southern parks.


Table 7. Estimated value of camping to the recreationist group: Southern
Florida state parks

Value Value per Value
Time of year per month 12 hours per visit

(1) (2) (3) (4)

Low season (S = 0)... $12.49 $10.05 $62.49

High season (S = 1).. 13.36 10.75 66.81

Total year (S = S)... 12.93 10.40 64.89


SOURCE: Sample data.


Illustration of a Value-Based Fee Policy

The large difference between estimated low-season and high-season usage

and value of recreation at the northern parks raises questions about the

appropriateness of equal interseasonal fees for those parks, or, at any rate,

constitutes the most obvious example of where a significant change would be

required to make fees reflect relative interseasonal values. It may be useful

to consider an alternative policy, if only to illustrate the calculation pro-

cedures involved in application of the model to such policy questions. Accord-









ingly, for purposes of the following illustrative example, it is assumed that

the criteria of a new fee structure for the northern parks are: (1) the dif-

ference between low-season and high-season fees should closely reflect the

estimated difference between low-season and high-season value received per

visitor, and (2) the new fee structure should, ceteris paribus, produce the

same total revenue per year as the present structure.

According to the seasonal vatluc estimates, the first criterion would be

met by setting the high season fee, U11, approximately 50 percent higher than

the low-season fee, U01, i.e.:


(37) U11 = 1.5 U01.

The second criterion is that the change in revenue per year should be zero,

i.e., R0 = -R1, where R0 is low-season total revenue per year and R1 is high-

season revenue per year. Expressed in terms of fees and usages, this relation-

ship becomes:


(38) 7 U01Ds01 01 7 U00D0s00G0 = -5 U11DsllG11 + G U10DsloG10'

where the first numerical subscripts refer to the season (0 = low-season; 1 =

high-season), and the second numerical subscripts refer to values before (sub-

script = 0) and after subscriptt = 1) the change in fee structure. For example,

D510 is the high-season usage per visitor-group before the change in the high-
season fee. The Gij are the total numbers of visitor-groups per month; for

example, G01 is the total number of groups visiting, per month, during the

low season after the change in the low-season fee. The U.. are the fees in
Sth
effect during the i-h season under the jt- fee structure. The weights, 5 and

7, are the number of months in high season and low season, respectively.









The usages per visitor, Dsij, are expressed as functions of the Uij as

follows, given the elasticity of use with respect to on-site cost which, from
Equation (25), is -.323:
(E
(39) D01 Ds00 = -.323 Es Eso 0) D

([Asl + Ul1 [AO+ U00])


(E EsO)
011 )10
(40) Ds1 s0 = -.323 Es10 = D510

([As11 + Ull] [As10 + U10])
= -.323 A0 + UO 0slo"
s10 10


Given existing knowledge and/or fair assumptions about the values of the
variables, Equations (37), (38), (39), and (40) constitute a system which can

be solved for the fee structure that meets the hypothesized policy criteria.
The "known" data for this purpose are as follows:
(1) U00 = U10 = $2 per 12-hour period (the present fee is the same
for both seasons).

(2) G G1 = 19,236 visitor-groups per month; G =G 10,960
10 11 (the number of visitors per month R assued to be
independent of the fee change).

(3) As01 = As00 = As1 = A10 = As. (It is assumed that ancillary on-
site cost per group is the same in both seasons, and
invariant with respect to the fee change.)

(4) DsO0 = 1.72 12-hour periods per month; D = 2.96 12-hour
periods per month (from the sampll~lata).

(5) E 00 = Es10: $9.66 (which follows from (1) and (3) above). Sub-
stitution of these data into Equations (38), (39),
(40), and (37), respectively, yields the system:


U01(76,270 Dso0 + 144,270 Ds11) = 833.302.4.


(41)









(42) Ds01 + .058 U01 = 1.835.

(43) Ds11 + .099 U11 = 3.158.

(44) U11 1.5 U01 = 0,

which reduces to the quadratic equation:

(45) 25,010. U012 -' 595,560 OU .+ 833,;,.'.4 = 0.

The solution is as follows:

U01 = $1.50 per 12-hour period

U11 = $2.25 per 12-hour period

Dso0 = 1.75 12-hour periods per month
Dsl1 = 2.93 12-hour periods per month.

In summary, a reduction of the northern park low-season fee to $1.50 and

an increase in the high-season fee to $2.25 per 12-hour period would, other

things remaining equal, leave total yearly revenue unchanged, and approximately

equalize the estimated value received per fee dollar spent in each season. The

estimated effects on campground use (barring significant effects on numbers of

patrons) would be a decline of approximately 1 percent in high season and an

increase of approximately 2 percent in low season. In terms of absolute mag-

nitudes, this would represent a decline of approximately 2,900 high-season

visitor-group-days, and an increase of approximately 2,300 low-season visitor-

group-days at all northern park campgrounds, for a net estimated decline in

total yearly usage of around 600 visitor-group-days.










SUMMARY AND CONCLUSIONS

Summary


The objectives of this study were (1) to develop a general model of the

individual recreationist's demand for particular facilities; (2) to test the

appropriateness of the model by estimating parameters of the model with data

pertaining to campers; and (3) to illustrate applicability of the empirical

model to informational needs of recreation facility planning and management.

The approach taken has been to use some component of recreationists' actual

costs as a proxy for the price of a facility. On consideration of comparative

characteristics of travel and on-site cost, the daily on-site cost was selected

as the facility price proxy, while letting travel cost play a different role

as a separate explanatory variable.

The basic model consists of two structural equations explaining length

of stay and frequency of visits, along with the identity from which the use-

per-time-period equation is derived. Applicability of the model to both single-

distination and multiple-destination recreationists was achieved by introduc-

tion of an adjustment factor applied to travel cost. Other specific problems

dealt with include the possible role of leisure-time constraints and alterna-

tive specifications of the recreationist decision unit.

The general study area consists of Florida state parks with campgrounds.

The state was divided into two areas, viz., parks north and south of Orlando,

Florida. A sample of parks was then selected to represent each area, thereby

providing two essentially different groups of facilities for separate analysis.

A sample of past campers was chosen for each group of parks, and person-

ally interviewed by telephone. From the telephone survey, camper registration









cards, maps, and calendars, data were obtained on all of the variables in the

statistical model, which were then estimated by multiple linear regression.


Conclusions


The principal empirical results are estimates of the structural equa-

tions explaining length of stay and frequency of visits. It makes little

difference to the estimates whether on-site and travel costs are specified

as per-person costs or per-group costs. In general, the algebraic signs of

the statistically significant coefficient estimates conform to expectations

based on theory and previous empirical research.

The travel-cost adjuster performs statistically well in the length-of-

stay equations by comparison with alternative specifications using unadjusted

travel cost. Performance in the frequency-of-visits equation is equivocal,

however, and this relationship is apparently subject to considerably greater

unspecified influences than is the length-of-stay relationship.

The question of whether a leisure-time constraint need be explicitly

considered was approached by asking the recreationists directly (the only

departure from the indirect method). Less than 10 percent of the 357 campers

queried answered that limited time primarily restricts their recreation in

the Florida state parks. It is thus tentatively hypothesized that leisure-

time constraints are not a serious issue for this study area.

Examples of using the estimated models to provide information of interest

to recreation planners and policy makers included the prediction of the effect

of a general change in on-site cost on use of the two groups of parks. The

reader was advised, however, that the elasticity of use, with respect to a

general change in on-site cost, is probably less than with respect to a use-










fee change unless certain conditions hold; namely, facility uniqueness and/or

vigorous price competition from private substitute facilities.

Value per visit was calculated from the derived Ds relationships, with

average magnitudes fixed for on-site cost and the seasonal shift variable.

For the northern parks, estimated value per visit during the winter season

was calculated at around $35.01 per group; during the summer season, estimated

value was around $55.12 per visit per group. For both seasons averaged, the

northern parks produced an estimated value of around $45.86 per visit per

group. For the southern parks, where seasonal differences were negligible,

the estimated value per visit was $64.89 per group.

The daily equivalents of the value estimates are of interest, since camp-

site fees are a group daily levy. For the year overall, the estimated value

per 12-hour recreation day in northern parks was $8.95 per group. The cor-

responding estimate for a winter's day in the northern parks was $6.25; for

a summer's day, the estimated value was $10.77. Thus, the estimated value

of a summer's day is around 53 percent higher than the value of a winter's

day in the northern sample parks.

Combining the estimates of value with the estimated yearly number of visi-

tors to the parks yielded an estimated value of all northern parks per year of

$14 million, while southern parks are estimated to be worth around $14.4 mil-

lion per year to campers.

Limitations


A major limitation of this study is one that afflicts all previous re-

search in the demand for public recreational facilities; namely, the assump-

tions that must underlie the use of some ancillary cost of recreation as a










proxy for facility price. In the early .stages of 'ocy):eptualizing this project,

the authors had hoped to exploit the rare occurrence of an actual -and substan-

tial increase in a calmpinq fee, which was envisioned as an additional shift

variable to be estimated frvin ddta on recreationists who camTp-.: both before

and after the fee increase. More evidence might thi~r ha.s be,"i :-.;..led about

the relative magnitudes oF the elasticities with respNc.t to the ancillary on-

site cost and the use fee. Ihis was not possible, hnw~ver. It is worth hI-ping

that in the future other scholars will be on the alert for such rare oppor-

tunities, and exploit them while they exist.

Although it is generally accepted that. the individual c.nsumner is the

basic unit of study for consumption and demand analysis, it is clear that be-

havior of the average recreationfst explains only a part of the observable

variation in aggregate demand. The absence of an equation explaining the

numbers and behavior of potential patrons thus constitutes a limit.:tiun in-

sofar as predictions of aggregate demand may be sought.

No adjustment was made li the travel and on-site costs to clnopensate For

the normal subsistence components of those costs. Thus, in theory thp on-

site cost is an upward-biased facility price proxy, even if the condition of

equal site specificity is otherwise met. The problem of determoiihg the sub-

sistence costs of campers is not, however, one on which any sin.ific.'ant break-

through seems imminent. Another approach, which has yet to be tried, might

be the decomposition of travel and on-site costs into further separate ex-

planatory variables. For example, transportation and lodging costs each may

exert different influences. Some components of ancillary on-site cost may be

better facility price proxies than others. The cost of food, which can he

eaten anywhere, is probably less appropriate than the cost of running one's










boat on a Platicular lake, for example.

Better estlmtes of the visits relationship would pr-bebly result f~v.r

taking into account alternative opportunities within .h.M vicinity o' the visi-

tor's residence. To an extent, the availability of alternatives aTrog the way

are acrountpd for by t!i travel-cost a,.juster which, in its ,., L-.;. t form, how-

ever, could unquestionably stand some theoretical refinement.

The ',amIple is biased in favor of recreationists who had telephones and

li;:ed number, and who .',re' at home and willing to answer the o...M-ir:nnire

when alled. Also, the .i.:vey took three months to i -ntrview a i'.smpri-' f past

campers sipa i'ning a year's time. It may have been preferi.ble to have ;:iedulled

the survey so as to minimize the memory time of the re:pundencts Probobly the

best wa.y to minimi-.e saimpi'l his.es of these types Is by means o'- :n. %i 1e per.-

sonal interviews. The telephone ,is, by comparison, a considerably cheaperr

dta ta- yj.hring device.

While not a real limit3 o, 'fihe derivation of prpdictlcn' ir.om estimated

*:x.~~.or,,,.ial s u.!.ii'.-tions is all too commonly done in a mri ne! tl ir, i'v-es both

b ed Pred.i :.io; and g ns'ly maiMfi d prediction v-,r'. S p'uh 4oul be the

results of drieivi ng predictions by direct substitution of hypothetical vliies

of the indrepr:ndent variables. The elasticity estimates alone c*-nnfain aIpe

inrfo i)rm !.-.ri .i';n iorc.:t predictive lpurpo e ,e. and should be used wlenever P.os lble

in the n' hi;, ;i ...,'; '. *o' c le, .. ti. i i ra, ion o. a 'i .s :ba ed fee

policy.









VtF TI- rpu !

[1] American Automobiln As socr iation. Ala 0000
ton, DC: 19N.

[2] Browni, William G., Agr Si"l4, .wij 'r!rv N. Castle. An e roiojrmicic
Evauaio o Lv ul ;OluoIn AIhin00
Sept;. 1964l.
[3] Burt, Oscar and Durwood Bir:'i, "Es timation of rH'9Va'ial "Aefits
from Outdoor [:.tra tion," %Wk.i rica 10:5 ( 1971). v. 8ll; -8V8.

[43 Clawson, Marion. 0093y, j t V. at


[53 Clawson, lidriLu i-a'hi Jack L. Knetsch. truww.u3 of vhomv r-tctin.'
Bal1timnore : 1he 3411 ln~ Honkino P.,

[6) Edwards, J. A., K. C. Gibbs, L. J 6WOT.l aO N N. 40t...10







1972ih~, ..---,r:) -
Demandoi 'fy cl'utiii n -v~,Th ik~ .*~I,?





po'vljc i~lt n f IhI~tc" Qualf i y n 1 .IItei I~: U~lt; ti. '1: An~ [YPi i cation
of~~ a I~ .~.d iqy Ou Mo We Lieq t in OW or Or 01'. ae Heai on
6'i, \701 -I I- --, I -it~IJ;i~;-;j~r ~31nI ~115





[10] Gibbs, Kenneth C, nd 3, ftachard of Gieru:i, Pll'rslioq ,fro no I
Creationail iVoii urs: Vissimme i ai, Flor i.'
1A~i [ul, : 1 (duly I197S;), 0 ~~-230'.

[11)3 Hendeiro., dom~ies Ni, end Vi.;harr E. Qwao~dk. HI:r~roic1I~~ A


[12) Hi cks, J. h A Revjision or Deumaind 1 hi-or". l'x ard: 1 h ClaruniPyn Press,
~121

[13] Hotel 1 I H rIoIc ld. L4..ttc'i cid ld '"l!e FH::no.i cs N ahli c Recradtiion:
An Ernumi-n iI S1ud y of t h~ ke Herietdy Ev:a 'xi on & f lecr~eati r. in the
[N1rkvnr Park,".. Wh'~1Wlultu, w;: 'U.S.- Novio wri nk Sorvic~e,
1 vt









[14] Howard Johnson's Motor Lodge & Restaurant Directory i!.iited Stjlat
International. Braintree, MA: Howard Johinsons Motor Lodgs,
T97i3.

[15] Jennings, Thomas A. "A General Methodology for Analyzing Demand for
Out-door Recreation, with an Application to Camping in Florida
State Parks." Ph.D. dissertation, Univ. of Fla., Mar. 1975.

[16] Jennings, Thomas A., and Kenneth C. Gibbs. "Some Issues Concerning
Specification and Interpretation of Outdoor Recreation Demand
Models," So. J. Agr. Econ. 6:1 (July 1974), 165-169.
[17] Knetsch, Jack L. and Robert K. Davis. "Comparisons of Methods for
Recreation Evaluation," in Allen V. Kneese and Stephen C. Smith
(Eds.). Water Research. Baltimore: Johns Hopkins University
Press, 1966, pp. 125-142.

[18] McGuire, John F. III. "An Application of Two Methods to Estimrtit
the Economic Value of Outdoor Recreation in the Kissimmee River
Basin." Unpublished Master of Science thesis, Univ. of Florida,
August 1972.
[19] Marshall, AlFred. Principles of Economics (8th ed.). London:
MacMillan & Co., Ltd., 1959.
[20] Oliveira, Ronald A. and Gordon C. Rausser. "Daily Fluctuations
in Campground Use: An Econometric Analysis," Am. J. Agr. Econ.
59:2 (May 1977), pp. 283-293.

[21) Pearse, Peter H. "A New Approach to the Evaluation of Non-Priced
Recreational Resources," Land Economics 44:1 (Feb. 1968), pp.
87-99.
[22] Rand McNally. Road Atlas: United States, Canada, Mexico. Chicago;
Rand McNIally & Co.,1973.

[23] Rausser, Gordon C. and Ronald Oliveira. "An Econometric Analysis of
Wilderness Area Use," J. Amer. Statis. Assoc. 71 (1976), pp.
276-285.
[24] Wilson, Robert R. "Demand Theory: Time Allocation and Outdoor Recrea-
tion," So.. J.Agr. Econ. 3 (Dec. 1971), pp. 103-108.






STATISTICAL AP'F'JPcDIX

Mean Values of the Variables for the
Samples of Florida State Park Camper, 1973


Northern park


Arithmetic mean
:s Southern parks


Dependent variables:
Length of stay per visit (D )
in 12-hour periods ............
In Dv .........................
Visits per month (V)...........
In V ..........................
Use ,er month (Ds V.D )......
Independent variables:
On-site cost per group (E ) per
12-hour period ...............
In E .......................
Travel cost per Group (Et).....
In Et ......................
Adjusted travel cost per
group (rEt) ...................
In (rEt) ......................
Visitor income (I).............
In I ..........., ..............
Group size (N), in persons.....
In (1/N) ......................
Seasonal dummy (S).............
Destination dummy (D)..........
Tent-camper dummy (X) .........
Additional visitor characteristics:
Minimum acceptable stay per visit
(Dvm) in 12-hour periods.......
In Dv ........................
Minimum round-trip travel time
(T1) in hours.................
Total time away from home (T2)
in 12-hour periods ............
Minimum 1-way distance, in miles


6.562
1.634
.370
-1.344
2.219


$9.661
2.140
$282.11
5.044


$153.72
4.470
$14,934.00
9.484
4.045
-1.293
.661
.712
.249


8.631
1.827
.232
-1.610
2.175


$8.623
2.028
$436.89
5.688


$193.12
4.850
$14,694.00
9.410
3.533
-1.152
.517

.667
.339


4.427
1.269

16.844

19.548
415


5.319
1.226

35. 68

34.133
950


SOURCE: Sample data.


Variable


I-


I ~ --- "-I-~~" "~ -









Correlation Matrix: Northern Parks


In(rEt)

0.3928

1.0000


rEtln Es

0.1830

0.5370

1.0000


In I

0.2243

0.2222

0.0807

1.0000


In(l/N)

-0.3155

-0.1575

-0.0258

-0.2996

1.0000


Source: Sample data.


In Es

1.0000


S

0.2717

0.1815

-0.0753

0.0977

-0.2732

1.0000


D

0.0547

0.1456

0.0753

0.1909

-0.2377

0.0715

1.0000


X

0.0555

0.0514

-0.0112

-0.1154

0.0894

0.0529

0.0484

1.0000










Correlation Matrix: Southern Parks


1n(rEt)

0.3260

1.0000


rE tnE

0.4867

0.7381

1.0000


In I

0.2306

-0.0115

0.0915

1.0000


ln(l/N)

-0.2738

-0.0623

-0.1471

-0.2848

1.0000


Source: Sample data.


In Es

1.0000


S

-0.1101

0.1055

0.0451

-0.0693

0.2612

1.0000


D

0.0348

0.1662

0.1342

-0.0958

-0.1655

0.1887

1.0000


X

0.0108

0.0120

-0.0249

-0.0949

0.0457

-0.0121

0.1328

1.0000




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