! I' \ KS-7 >- l'»7.»
Socioeconomic Environmental Studies Series
Economic Benefits from an
Improvement in Water Quality
Office of Research and Monitoring
U.S Environmental Protection Agency
Washinaton. DC 20460
-------
RESEARCH REPORTING SERIES
Research reports of the Office of Research and
Monitoring, Environmental Protection Agency, have
been grouped into five series. These five broad
categories were established to facilitate further
development and application of environmental
technology. Elimination of traditional grouping
was consciously planned to foster technology
transfer and a maximum interface in related
fields. The five series are:
1. Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research
*». Environmental Monitoring
5. Socioeconomic Environmental Studies
This report has been assigned to the SOCIOECONOMIC
ENVIRONMENTAL STUDIES series. This series
describes research on the socioeconomic impact of
environmental problems. This covers recycling and
other recovery operations with emphasis on
monetary incentives. The non-scientific realms of
legal systems, cultural values, and business
systems are also involved. Because of their
interdisciplinary scope, system evaluations and
environmental management reports are included in
this series.
-------
EPA-R5-73-008
January 1973
ECONOMIC BENEFITS FROM AN IMPROVEMENT IN
WATER QUALITY
By
S. D. Reiling, K. C. Gibbs, H. H. Stoevener
Project 16110 FPZ
Project Officer
Dr. Roger Don Shull
Implementation Research Division
Environmental Protection Agency
Washington, D. C. 20460
Prepared for
OFFICE OF RESEARCH AND MONITORING
U. S. ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, D. C. 20460
For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.O. 20402
Price $2,10 domestic postpaid or $1.76 OFO Bookstore
-------
Review Notice
This report has been reviewed by the Environmental
Protection Agency and approved for publication.
Approval does not signify that the contents neces-
sarily reflect the views and policies of the Envi-
ronmental Protection Agency, nor does mention of
trade names or commercial products constitute
endorsement or recommendation for use.
11
-------
ABSTRACT
This report introduces and empirically tests a new methodology for
estimating the economic benefits accruing to society from an improved
recreational facility. The specific facility under consideration is
Bfpper Klamath Lake, Oregon, which presently has low water quality.
The methodology draws upon previous work done in the evaluation of
recreational demand; however, it focuses upon the individual recrea-
tionist and separates the traditional price variable into on-site
costs and travel costs. The model is used to estimate the number
of days per visit the recreationist will stay at the site as the
water quality improves.
Data collected at three other lakes with varied characteristics are
used to derive a relationship between the number of visits to a site
and the characteristics of the site. This relationship is then used
to estimate the increase in visits to Klamath Lake that would be
forthcoming with an improvement in water quality.
The impapt of expanded recreational use of Klamath Lake upon the
local eponomy is also estimated through the use of an input-output
model of the Klamath County economy.
This report was submitted in fulfillment of Project Number 16110 FPZ
under the sponsorship of the Office of Research and Monitoring,
Environmental Protection Agency.
iii
-------
CONTENTS
Section Fage
I Conclusions 1
II Recommendations 3
III Introduction 5
IV A Theoretical Model to Estimate
Previous Work in Estimating the ,
Demand for Recreation ' 9
V Empirical Specification of the
Model 29
VI Estimating and Applying the Sta-\
tistical Demand Model 39
VII The Theoretical Model for Esti-
mating Regional Benefits 61
VIII Construction of the From-to
Model, and An Analysis of the
Local Economy 69
IX Application of the Input-Output
Model 83
X Economic Benefits of Water Quality
Imp rovemen t 93
XI Acknowledgements 105
XII References 107
XIII List of Patents and Publications 111
XIV Glossary 113
XV Appendices i!7
-------
FIGURES
Page
1 The Commodity Space for Commodities 0- and (^ 12
2 An Indifference Curve for Commodities Q.^ and Q2 14
3 An Indifference Map for Commodities Q, and Q2 15
4 The Consumer's Budget Constraint 17
5 Maximization of Consumer's Utility 19
6 Quantities of Q- Purchased at Various Prices 20
7 The Consumer's Demand Curve for Commodity Q, 21
8 An Illustration of Consumer's Surplus 23
9 The Optional Combinations of Recreation and
Non-Recreation, Given Travel Costs of k , k-, and
k for Given Prices p1 and p», and Fixed Income y 26
10 The Average Individual's Demand Curve, Per Visit,
for a Lake 56
11 The Average Recreationist's Demand Curve, Per
Visit, for Lake of the Woods 58
12 Klamath County, Oregon 70
13 The Average Recreationist's Demand Curve, Per
Visit, for Klamath Lake (Step 1) 95
14 The Average Recreationist's Demand Curve, Per
Visit, for Klamath Lake (Step 2) 98
vi
-------
TABLES
1 Estimated Use-Intensities for Certain Recreational
Activities and Lake Size, by Lake 33
2 lumber of Interviews Taken at Each Lake, by Block,
for the Four Time Periods 38
3 The Population, Number of Sample Visits, Percent
of Sample Visits, Visits Pet Season, Travel Cost,
and Income, by County, for Each of the Four Lakes 46
4 A Comparison of the Forest Service Estimates of Visits
to Each Lake in 1968, and the Estimates Derived from
the Visits Equation 54
5 A Hypothetical Transactions Matrix 62
6 Description of the Sectors in the Klamath County Model 71
7 Distribution of the Sample Among the Sectors of the Model 74
8 Transactions Matrix Showing Interindustry Flows in
Dollars, Klamath County, 1968 (Rounded to Nearest
$1,000) 77
9 Direct Coefficients Matrix, Klamath County, 1968 79
10 Distribution of Sales of Each Sector in the Klamath
County Economy 80
11 Direct and Indirect Coefficients Matrix, Klamath
County, 1968 84
12 Output and Income Multipliers and Income-Output
Coefficients for Each Sector of the Klamath County
Economy 85
13 Average and Total Travel Cost Incurred in Klamath
County, by Component, in 1968 88
1 i
14 Average and Total On-Site Cost, by Component, for
klamath Lake in 1968 89
vii
-------
No. Page
15 Total Recreational Expenditures and Percentages,
in Klamath County, by Sector, Associated with
Recreation at Klamath Lake in 1968 90
16 Projected Increases in Final Demand, Total Output,
and County Household Income, by Economic Sector,
Associated with Recreation at Klamath Lake in 1968 92
17 Hypothesized Use-Intensity Ratings for Klamath Lake
at the Present Time, and After Steps 1 and 2 93
18 Net Increase in Expenditures, for Each Component of
Travel Cost, Associated with Improvements of Water
Quality at Klamath Lake 99
19 Net Increase in Expenditures for Each Component of
On-Site Cost Associated with Improvements of Water
Quality at Klamath Lake 99
20 Projected Increases in Final Demand, Total Output,
and County Household Income, by Economic Sector,
Associated with Klamath Lake After the Completion
of Step 1 101
21 Projected Increases in Final Demand, Total Output,
and County Household Income, by Economic Sector,
Associated with Klamath Lake After the Completion
of Step 2 102
viii
-------
SECTION I
CONCLUSIONS
1. Improved water quality in Upper Klamath Lake, Oregon, would result
in expanded use of the lake for recreational activities.
2. A new conceptual model is developed and used to estimate the demand
for recreation at Klamath Lake. The traditional price variable is sepa-
rated into travel costs and on-site costs, because recreationists react
differently to changes in the two costs. When both costs are combined
in a single variable, the effects are dampened and only the stronger
effect is observed.
3. The methodology also focuses upon the individual recreationist in-
stead of the population of recreationists. This avoids the necessary
assumptions made in earlier studies concerning the characteristics and
homogeneity of the population groups.
4. A relationship is developed to explain the number of visits to a
recreational site with certain characteristics. This is accomplished
by utilizing data gathered at three other lakes which possess different
characteristics. The relationship is used to estimate the number of
visits to Klamath Lake after its characteristics are improved. The man-
ner in which the site characteristics are specified in the model is not
considered to be entirely satisfactory* The use-intensities for the
various water-related activities were used because the level of these
activities are, to some extent, dependent upon the water quality and
other physical features of the lakes. However, it would be more satis-
factory to specify the model with respect to the biological and physical
parameters of the lake directly, since the use-intensities may not depend
entirely upon the changing parameters of the lake. Unfortunately, the
necessary data were not available to specify the model in this manner.
5. It is estimated that, if the algae were removed from Klamath Lake,
the net economic value of the lake would increase by $1,200,000 per year.
In addition, the income of households in the county would increase
$194,000 per year.
6. If, in addition to removing the algae, the water temperature of the
lake were lowered and the beaches improved, the net economic value of the
lake would increase by an additional $2.65 million. Thus, the value of
the recreational benefits associated with the two-step improvement is
estimated to be $3.85 million per year, while household incomes would be
$542,000 higher annually.
-------
SECTION II
RECOMMENDATIONS
Because of the unique shape of the demand curve derived in the study,
more than one value can be interpreted to represent consumer's surplus.
It is not clear at this time which value is correct. Since the interpre-
tation used has such a significant influence on the final results, addi-
tional work on this problem is strongly recommended.
Throughout the analysis it is assumed that the expanded use of Klamath
Lake for recreation will not affect the level of use of other lakes in
the vicinity. This ignores the possibility of recreationists substi-
tuting one recreational site for another, and implies that the postulated
increase in recreation at Klamath Lake represents a net increase of
recreation in the area. This is, to some extent, an invalid assumption.
Additional research is warranted to determine the degree of substituta-
bility among recreational sites.
An attempt to incorporate the value of recreational equipment in the model
as a substitute for the recreationist's current income was not success-
ful. This effort was made because current income may not accurately re-
flect the recreational budget of the recreationist. Further work in this
area is suggested.
Future use of the model to predict the demand for recreation at a site
after its characteristics have been altered will require a better speci-
fication of the model with respect to these characteristics. Multi-
disciplinary work is clearly needed to accomplish this goal.
Most of the work done in determining the demand for publicly provided
outdoor recreation has focused on the estimation of the number of days
per visit "consumed" at a site. The problem of determining the number
of visits an individual will make to a site in a specified time period
has been ignored. Work in this area is needed because of the relation-
ship that exists between days per visit and the total number of visits.
A model which could determine both variables simultaneously would be
very useful.
This study represents only the initial test of the new methodology. Re-
finements and further tests are warranted, and are presently being con-
ducted.
-------
SECTION III
INTRODUCTION
Extensive research has been conducted by the staff at the Pacific North-
west Water Laboratory of the Environmental Protection Agency, on the
physical and biological aspects of the water quality problem of Upper
Klamath Lake. Aside from the strictly scientific benefits resulting
from this work, it is directed toward finding techniques which would
permit alteration of the biological processes in such a way as to im-
prove the lake's water quality and its usefulness to man.
Upper Klamath Lake is located in south-central Oregon, near the city of
Klamath Falls, which has a population of about 38,000 in its immediate
vicinity. It is the largest body of fresh water in the State, being more
than 30 miles in length and comprising a total area of more than 130
square miles. U.S. Highway 97 follows the eastern shore of the lake
north of Klamath Falls for about 15 miles. The highway is used by tour-
ists during the summer, since it is one of the principal routes to Crater
Lake National Park. Usually one would expect such an accessible body of
water to be a popular site for water-based recreation. However, this is
not the case at Upper Klamath Lake. Although the lake now supports a
limited amount of recreational activities, poor water quality renders
the lake undesirable for large-scale recreational use. The poor water
quality stems primarily from large concentrations of algae and warm water
temperatures during the summer months.
A brief examination of some of Klamath Lake's physical characteristics
may be helpful in identifying the present water quality situation. First,
mud deposits, ranging in depth from a few inches to more than 150 feet,
have accumulated on the bottom of the lake [Bartsch, 1968]. These de-
posits contain large concentrations of the primary nutrients necessary
for algae growth, particularly nitrogen and phosphorus.
The accumulation of mud deposits has also decreased the depth of the lake.
At the present time its average depth is less than ten feet. This pre-
cludes the formation of temperature stratifications and allows low wind
velocities to cause sufficient water movement to keep the needed nutri-
ents suspended in the water, where they can be utilized by the algae.
The warm water temperatures also limit the size of the sport fishery of
the lake. All of these factors adversely affect the water quality of
Klamath Lake and retard its use as a recreational facility.
The Economic Problem
The ultimate problem facing the economist is to estimate how much it is
worth to society to improve the water quality of Klamath Lake. Or, to
restate the problem in a more general way, what are the benefits that
would result from a water quality improvement at Klamath Lake?
-------
The benefits associated with water quality improvements at Klamath Lake
are primarily recreational benefits. Although recreation is only one of
many possible uses of land and water resources today, its importance is
increasing as leisure time and the level of family income continue to
increase* People appear to be willing to make considerable financial
sacrifices, in terms of travel costs to the site and equipment purchases,
to participate in outdoor recreation. Thus, the estimation of recrea-
tional benefits has become a very important factor in the evaluation of
natural resource projects.
Of the various competing uses for natural resources, the evaluation of
the economic benefits associated with outdoor recreation is especially
difficult. Unlike many of the other uses for natural resources, an ade-
quate market does not exist for outdoor recreation. That is, "outdoor
recreation" is not a commodity that is purchased and sold at a given
price. Instead, recreational resources have traditionally been con-
sidered a "free" commodity. This has necessitated the development of
other methods for evaluating recreational benefits. Several methods
have been used to estimate the demand for recreation with varying de-
grees of success. This study presents a method for estimating the de-
mand for a recreational site which is new in several important aspects.
Another problem confronting the economist is the determination of which
benefits should be included in the evaluation of a project. Other bene-
fits, in addition to the recreational benefits already mentioned, can
also be attributed to water quality improvements at Klamath Lake. For
example, as the quality of water improves and Klamath Lake is used more
extensively as a recreational facility, the local economy will be the
recipient of some economic benefits. As more recreationists use the
lake, additional goods and services will be purchased from the local
community. As business activity in the community increases, household
income will also rise. Thus, the community benefits indirectly from the
improved water quality. The indirect or "secondary" benefits differ from
the recreational benefits in that the latter accrue to the nation as a
whole, while the former, as measured in this study, accrue only to the
local region. Depending upon the prevailing conditions in the local and
national economies, all or a part of the secondary benefits may also
accrue to the nation as well as to the local region. However, it is
difficult to determine the magnitude of the secondary benefits that should
be included in the national accounts. The theoretical and empirical issues
in the determination of secondary benefits, given the national viewpoint,
are discussed in Seattle [1970, pp. 76-93], and will not be reconsidered
in this study.
Estimation of the regional benefits may provide other useful information.
For example, the local community may be willing to pay part of the cost
of the project. The magnitude of secondary benefits would set the upper
limit to the local community's willingness to participate in such cost
sharing. Also, estimation of the regional secondary benefits is a pre-
requisite for estimating the level of these benefits that may be relevant
from the national viewpoint.
-------
Objectives
The specific objectives of this report are four-fold. The first is to
present a methodology appropriate for determining the economic benefits
accruing to society from the development of a recreational facility.
The second is to determine the relationship between water quality and
recreational use of a facility by using the new methodology. This mafyes,
it possible to predict the change in recreational use that would accom-
pany a substantial improvement in water quality.
The third objective is to determine the economic benefits accruing to
society in general as a result of water quality improvements and the
associated increase in recreational use of Klamath Lake. The final ob-
jective is to estimate the benefits that would accrue to the local econr
omy as a result of the hypothesized increase in recreation at Klamath
take.
As the objectives indicate, the research presented in this report serves,
two purposes. First, it provides specific information concerning the
feasibility of allocating public funds for water quality improvement £n
Upper Klamath Lake. Second, and perhaps more important, is the evalua--
tion of the methodology presented herein, so that it may be applied to
the estimation of recreational benefits resulting from water quality
improvements at sites other than Klamath Lake.
Organization of the Report
The next two sections consider the theoretical concepts involved in the
estimation of demand relationships for outdoor recreation. Conventional
economic demand theory, and some of the previous work done in estimating
the demand for outdoor recreation, are reviewed in Section IV. These
topics provide the background necessary to introduce the new model used
in this study. The theoretical model is also presented in Section IV.
Section V contains a discussion of the statistical model for recreational
demand. Each variable in the model is discussed. Sampling techniques
and measurement problems are also described. The application of the model
is made in Section VI.
Section VII explains the procedures used to estimate the local economi^
impact of increased recreational use of Klamath Lake. Since input-ou|put
techniques are used to quantify the regional benefits, the theory of
input-output analysis is explained briefly. The model of the Klamath
County economy is also presented in Section VII.
Sections VIII and IX contain the empirical analysis and the results qf
the input-output study. Finally, the effects of two hypothetical impirovew
ments in water quality of Klamath Lake are estimated in Section X. This
section utilizes the results obtained from the demand analysis as well
as those resulting from the input-output study.
-------
SECTION IV
A THEORETICAL MODE7! TO ESTIMATE RECREATION DEMAND
Previous Work in Estimating the Demand for Recreation
Many outdoor recreational services are provided publicly. As the supply
of these services has not relied upon the market system, the economic
evaluation of the benefits derived from the consumption of outdoor recre-
ation cannot depend upon the methods relevant for evaluating market
goods. A different set of techniques has to be developed.
The estimation of the value of outdoor recreation has proceeded in two
general directions. Both seek to determine the amount recreationists
are willing to pay to be able to use a certain facility. One approach
is the "direct" method of estimating the consumer's willingness to pay
[Knetsch and Davis, 1966]. The recreationists are asked, by means of a
personal interview, to state how much they would be willing to pay for
the use of the recreational facility, rather than be excluded. The de-
mand estimates obtained in this fashion are defensible on theoretical
grounds, but the degree of reliability which can be placed upon the re-
spondent's answers is often difficult to determine. Biases are likely
to exist, especially when questions are asked which deal with matters of
opinion concerning a person's activity that has customarily been regarded
as "free".
One source of bias is the consumer's understatement of his preference for
a facility if he fears that a charge may be levied for future use of the
facility. He may feel that understating his level of benefits may enhance
his possibility of enjoying the facility in the future while paying some-
thing less than his actual willingness to pay. On the other hand, if the
recreationist feels that the recreational service in question will con-
tinue to be publicly provided without the levying of user fees, he may
overstate his willingness to pay. In doing so, he may expect to combat
competitive pressures for non-recreational uses of the facility and thus
support the case for improvement and/or preservation of the recreational
site.
One advantage of the direct method is that it is not restricted to esti-
mating only the effective demand for outdoor recreation. It can also
estimate the demand of those people who are not participating in the
activity at the present time, but who may wish to participate at a later
date. These people would be willing to pay to preserve the option of
participating in the future. Unfortunately, measurement problems are
also present here because of the hypothetical nature of the questions
posed to the prospective recreationists.
The second approach for determing the amount recreationists are willing
-------
to pay for the use of recreational facilities relies upon the reactions
of recreationists to changes in costs of participating in recreation at
the recreational site. Willingness to pay can be computed from this
"indirect" evidence. The procedure is limited in that inferences must
be made to the entire population consisting of recreationists and non-
re creationist s ; only the effective demand can be analyzed. This approach
is utilized in this study.
Hotelling, in a letter published by the U.S. National Park Service in
1949, defined concentric zones around a recreational site in such a way
that the cost of traveling to the site from a given zone would be approxi-
mately constant. His suggestion was to use the travel cost that existed
within each zone as the price variable to be compared to the number of
visitors from each zone. A demand function for recreation could then be
obtained.
Although Clawson [1959] recognized problems in this formulation, he used
the basic idea underlying Hotelling's approach and gave it an interpreta-
tion that further facilitated the measurement of recreational values.
Clawson envisioned deriving two demand relations. The first was expressed
as a relationship between the level of travel cost and the rate of parti-
cipation of a population group derived in the manner suggested by Hotel-
ling. From the first demand relation he derived a second demand schedule.
The rate of participation from a given population group, for a certain
fee increase, was predicted by referring to the observed participation
rate of another population with travel costs equal to the travel cost of
the group in question, plus the fee increase. A demand schedule for a
population group was obtained by relating various fee increases to the
resulting participation rates. The participation rates were multiplied
by the number of people in the group to estimate the quantity of use from
that population group. This procedure was repeated for each zone, and the
resulting demand schedules were added horizontally to obtain the aggre-
gate demand schedule for the recreational resource.
Brown e£ al. [1964] and Stevens [1966] further refined the Clawson model
by incorporating income and the quality of the recreational experience
into the model. Angling success per unit of angling effort was added as
an independent variable. Work was also done on the inclusion of distance
as a separate explanatory variable. However, it was found to be highly
correlated with transfer costs, due to the manner in which transfer costs
are defined.
Many important and restrictive assumptions are involved in the indirect
approach discussed up to this point. First, it is implied that the re-
actions of recreationists to a fee increase would be identical to an
equal addition in the cash cost of travel. No distinction is made between
a recreationist's reaction to increased variable costs (daily costs while
at the recreational site) and increased fixed costs (costs of travel).
Secondly, in predicting a group's response to a change in costs by ob-
serving other groups, it is assumed that all of the groups, stratified by
distance, face identical alternatives to the recreational resource in
10
-------
question. Thirdly, it is assumed that recreationists are the same in all
other respects, in all distance zones, so that they will react in the
same way to increases in the cost of travel.
This study presents an extension of the indirect approach to the evalua-
tion of recreational resources. It should be noted that, independent of
the construction of the theory found in this section, Fearse [1968] de-
veloped a very similar approach. His approach differs slightly in the
technical development, and his application is entirely different. The
theoretical development of the procedure used herein will be examined,
with the focal point being the individual recreationist instead of a
population group. This eliminates some of the restrictive assumptions
made about the population groups in the Clawson method.
Conventional Demand Analysis
Before presenting the theoretical model used in this study to estimate
the demand for recreation, it may be helpful to review the fundamental
concepts of demand analysis. Economists and others familiar with demand
theory may wish to proceed directly to the subsection entitled "The Theo-
retical Model Applied to Outdoor Recreation". Let us begin by assuming
that there is one consumer and two commodities, Q- and Q.. It is also
assumed that the consumer prefers to have as much of each commodity as
possible; that is, both commodities are considered desirable by the
consumer. The objective of the consumer is to maximize his satisfaction,
subject to a constraint - the amount of money he has available to pur-
chase the two commodities in a given time period.
All possible combinations of commodities Q, and Q~ the consumer could
conceivably choose, if he were not constrained by a budget, can be en-
visioned in Figure 1 as lying above and to the right of the origin. This
is referred to as the "commodity space". Every point within the commo-
dity space represents a combination of commodities Q. and Q~ that may be
consumed.
The consumer is confronted with an infinite number of combinations in the
commodity space. It is assumed that the consumer has the ability to rank
all of the combinations in the commodity space according to the level of
satisfaction that he receives from each of them. All of the information
concerning the consumer's satisfaction is contained in his utility func-
tion. A utility function expresses the relationship between satisfaction,
or utility (U), and the quantity of commodities Q- and Q2 consumed:
U = U(q;L, q2) (1)
where q, and q~ refer to the amounts of Q. and Q2 consumed. It is also
assumed that the consumer is consistent in his rankings; if he prefers
Combination B to Combination C, and C to A, he must also prefer B to A.
Indifference curves are a helpful analytical device. They are obtained
11
-------
B
12 3
Figure 1. The Commodity Space for Commodities Q, and
12
-------
by holding the level of utility constant, and observing the various
combinations of the commodities that are consistent with the fixed level
of utility.
Uo = U(V q2> (2)
where U refers to a constant level of utility. The indifference curve
depicted by Equation (2) is shown in Figure 2.
The indifference curve shows the different combinations of Q, and Q~
that yield equal satisfaction to the consumer; he is indifferent, or
has no preference, between the combinations of Q, and Q2 that lie on the
indifference curve U .
o
It should also be noted that all combinations of Q. and Q. which lie
above and to the right of U are preferred to those combinations along
U , since the consumer enjoys more of at least one of the commodities.
For example, Points 8 and C in Figure 2 yield a higher level of satis-
faction than Point A, since the consumer has more of one commodity and
the same amount of the other. Therefore, Points B and C must lie on
higher indifference curves. Likewise, all points below and to the left
of U are less preferred combinations of Q, and Q7 than those located on
U . ° ,
o
The indifference curve U in Figure 2 represents only one of an infinite
number of indifference curves for the consumer. Figure 3 contains a
portion of the indifference curves defined by the consumer's utility
function. This is referred to as an indifference map. Again, the curves
above and to the right of another indifference curve represent higher
levels of utility or satisfaction to the consumer.
Some of the more important properties of indifference curves should be
noted. The shape of the indifference curve can be ascertained from the
total derivative of Equation (2):
au . . au . ,0,
dUo = 3^ dql + 3q^ dq2 (3)
Setting Equation (3) equal to zero and solving for dq^/dq., yields:
j /j 3u / 3u (,\
dq2/dql = " 3^ ' 3q^ (4)
Equation (4) represents the slope of the indifference curve. Since the
consumer prefers to have more of both commodities, 9U/3q. and 3U/3q are
positive. Therefore, the indifference curve has a negative slope. The
second derivative of the utility function is positive, which means the
curve is convex to the origin.
Another point worth noting is that indifference curves cannot intersect.
13
-------
1234
Figure 2. An Indifference Curve for Commodities Q.. and
>- Qi
14
-------
Figure 3. An Indifference Map for Commodities Q. and Q-,
15
-------
Since the curves reflect different levels of satisfaction, two curves can-
not share a single combination of commodities. Two curves passing through
the same point indicate that one combination yields two different levels
of satisfaction to the consumer. Since it is assumed that the consumer
has the knowledge to rank all of the combinations of commodities in the
commodity space, such inconsistencies cannot exist.
Now that the concept of indifference curves has been introduced, let us
return to the commodity space. It contains all possible combinations
of commodities Q- and Q« that the consumer could conceivably consume.
However, it may not be possible for the consumer to choose all of the
points in the space, since he is constrained by the amount of money he
has available to purchase the two commodities.
To determine the consumer's attainable set, assume that he has M^ dollars
to spend on commodities Q., and Q2- If the consumer chooses to purchase
commodity Q. only, he can obtain M./p1 units, where p. represents the
price of commodity Q-. Similarly, if he chooses to purchase Q. only, he
can obtain M /p units. The budget constraint faced by the consumer is:
Ml = qlpl + q2p2 (5)
Equation (5) is illustrated in Figure 4. The consumer is able to pur-
chase any combination of the two commodities in the set bounded by the
horizontal and vertical axes and by the line representing Equation (5).
This portion of the commodity space represents the consumer's attainable
set. The slope of the budget constraint can be determined from Equation
(5):
dqjL P2
From Equation (6) and Figure 4, it can be seen that a change in the
price of either commodity will change the slope of the budget constraint
line. However, a change in the consumer's money income will cause a
parallel shift of the budget constraint.
We are now ready to determine the "most preferred" combination of commo-
dities Q.^ and Q2- The consumer will choose the combination of commodi-
ties Q., and Q2 to maximize his utility, given his income constraint. This
is equivalent to maximizing the following function:
" qlpl " q2p2} (7)
where X is the Lagrangian Multiplier. The conditions for maximizing con-
strained utility are fulfilled when the partial derivatives of Equation
(7), with respect to q^, q2> and X are set equal to zero:
9y 3u
K ** n Ap_ = 0
3*! 3qx i
16
-------
qlpl + q2P2
Figure 4. The Consumer's Budget Constraint,
M,
17
-------
\/ V v ^J ^ /%
3q0 3q_ P2
/ f.
3V=M_ _qp=0
3X 1 11 22
The consumer maximizes his constrained utility by consuming those quanti-
ties of 0^ and Q2 that satisfy Equation (10) and the following first-
order condition:
3U /3U Pl
3q2 ~ ?2
That is, Q- and Q2 will be consumed until the ratio of their marginal
utilities equals the ratio of their respective prices, and all income
is spent.
The maximization of constrained utility is illustrated graphically in
Figure 5. The consumer's budget constraint is superimposed on his in-
difference map. Money income is M-, and the price of commodities Q^
and Q2 are p. and p2, respectively. Indifference curve U2 represents
the highest level of utility that is attainable with the given budget ,
constraint. Therefore, the consumer will maximize his utility by con-
suming q? units of Q., and q? units of 0_.
The Demand Curve
The consumer's demand curve for a commodity is derived from his indif-
ference map. A demand curve is a schedule that shows the various quan-
tities that the consumer will purchase at various prices.
Assume the price of commodity Q_ and money income are fixed at p? and
M. , respectively, while the price of commodity Q- is varied. As shown
in Figure 6, the quantity of Q., purchased will vary as its price varies.
When the price of Q- is p9, the consumer will purchase q9 units of the
commodity. When the price of QI increases to p' and p", the individual
will purchase only q! and q2 units, respectively. Thus, as the price of
Q. increases, the consumer purchases less of the commodity. The indi-
vidual's demand curve is derived by plotting the various prices and the
respective equilibrium quantities purchased, as shown in Figure 7.
It should be noted that the derivation of the demand curve is contingent
upon the continued optimizing behavior of the consumer. This is illus-
trated by the tangencies at Points A, B, and C in Figure 6. Any changes
in the consumer's utility function, income, or the price of commodity
Q2 will shift the individual's demand curve for 0^. A market demand
curve for a commodity is obtained by horizontally adding the demand curves
of all individuals in the market.
One other concept needs to be discussed before introducing the demand
model f)br recreation. It is "consumer's surplus". Let us begin with
18
-------
u.
Figure 5. Maximization of Consumer's Utility.
19
-------
u.
1 \ V-^X
1 \ «\^
1 l\ 1 \
I 1 \ 1 \
. U2
V ui
\
\
*i qi!i q° !i ^L
ii * _ i "_
Figure 6. Quantities of Q. Purchased at Various Prices.
20
-------
o
PI
Quantity of Q,
purchased
Figure 7. The Consumer's Demand Curve for Commodity Q,.
21
-------
the notion that a consumer pays a price for a commodity that is less than
or equal to the benefit he receives from the commodity. This can be
illustrated by an individual's demand curve DD, as shown in Figure 8.
Assume that the market price for the commodity is two dollars. At that
price, the consumer demands five units of the commodity. He pays two
dollars for each of the five units of the commodity. However, the con-
sumer's demand curve shows that he would be willing to pay more than two
dollars for the first unit of the commodity. In fact, the consumer would
be willing to pay six dollars. However, since the first unit, like all
other units, is sold at the market price of two dollars, the consumer
receives six dollars worth of satisfaction for only two dollars. Thus,
he enjoys a "surplus" by receiving excess benefits from the first unit.
The same situation exists for the second, third, and fourth units of the
commodity; the consumer is paying less for those units than he would be
willing to pay. Therefore, those units of the commodity result in a
surplus to the consumer. The difference between the price the consumer
is willing to pay for the units of the commodity and the price he actually
has to pay for them is called "consumer's surplus". Consumer's surplus
is used later in this study to estimate some of the values associated
with the demand for outdoor recreation.
The Theoretical Model Applied to Outdoor Recreation
To analyze the economic behavior of recreationists, it is necessary to
derive a model which will account for the number of visitor-days recrea-
tionists will take at various levels of expenditures. This will require
a slight alteration of the conventional demand analysis outlined above.
The theory conceptualized in this section comes from an unpublished paper
by Dr. John A. Edwards, Department of Agricultural Economics, Oregon
State University.
In the presentation above, it was assumed that to purchase a unit of
either commodity, the consumer had to pay the relevant prices, p- and p...
Now suppose the consumer must pay, in addition, a certain charge, or cost,
referred to as k, in order to buy any units of Q . However, the value
of k does not depend on the amount of Q. purchased.
Recreation is a good example where k is relevant. In order to enjoy any
amount of recreation, Q., the recreationist must incur a certain price
per day, p., while recreating. However, he must also travel to the re-
creational site. The travel costs, including the transportation cost,
food, lodging, camping fees, etc., that occur while enroute to and from
the recreational site, do not depend upon the quantity of Q. consumed,
and will be referred to as k. *
The recreationist will allocate his income in order to maximize his util-
ity, U:
U = U(qr q2) qlf q2 >_ 0 (12)
where q-j^ indicates the number of recreation-days the recreationist en-
joys at a particular site per visit, and q2 represents the amount of all
22
-------
Price ( )
M
Quantity
Figure 8.
1234567
An Illustration of Consumer's Surplus.
23
-------
other goods and services the recreationist could purchase with his in-
come. The recreationist is again limited to a fixed budget, which im-
poses a constraint upon him. It is recognized that the recreationist
also faces a time constraint and, in some cases, this may be more severe
than his budget constraint. However, the time constraint is not con-
sidered explicitly in this analysis.
The income, y , allocated to the consumption of the two commodities must
just equal the total amount spent for the recreation-days commodity,
p.q. + k, plus the total expenditures for the non-recreation-days commo-
dity, Pq:
yo » p^ + k + p2q2 yo, PI, P2 >_ 0; q.^ q2» k > 0 (13)
Thus, the recreationist will maximize the Lagrangian function
V - U(qlf q2) -I- X(yo - p^ - k - p^) (14)
by consuming those amounts of q^ and q2 that satisfy the budget constraint
and the following first-order condition:
The consumer will consume recreation and non-recreation up to the point
where the ratio of the marginal utilities associated with recreation and
non-recreation is equal to the ratio of their respective prices.
The budget constraint can be rewritten as:
yo - k - p^ + p2q2 (16)
Equation (16) more clearly illustrates the importance of k. It reduces
the income available to the consumer for purchasing the commodities. It
is assumed that k can be equal to zero if, and only if, no recreation is
consumed :
k - 0 <==> qx 0.
This assumption points out a unique characteristic of the budget con-
straint. If k - 0, the budget constraint takes on a new form:
yo * P2q2 for V P2' - 0; q2 >
0;
If faced with the budget constraint given in Equation (17), the consumer
would maximize his utility by taking as many non-recreation units as his
income would allow; he would consume q9 * y /p7 units of Q-, and no units
of recreation, Q.. °
24
-------
Variations in Travel Cost (k)
The indifference map and budget constraints of a typical consumer are
presented in Figure 9. The two prices, $i and p2, and the level of income
are held constant. The only variation in the budget constraints is due to
changes in k. The budget constraint BC is one for which k = k , a large
positive value. The point on the vertical axis at q2 - y /p° illustrates
the discontinuity in the budget constraint. If the consumer allocated
all of his income to the consumption of non-re ere at ion, he could attain
the position y /p«, since he will not have to withstand the additional
Q £ il-.l-.L-l-L
travel cost required to enjoy recreation, as he must at all other points
on budget line BC .
Given the set of indifference curves and the budget constraint BC in
Figure 9, the consumer will prefer the combination {q.. = 0, q_ - y /p°}
over any other attainable combination. He will enjoy a level of utility
of U-. If he chose any other attainable set of the commodities, he could
attain only a level of utility of U .
If the travel cost were less than previously considered, say k - k , the
consumer would be faced with the budget line BC. in Figure 9. Shifting
the budget line to the right indicates the availability of more income
to allocate to the two commodities; k - k. more dollars are available.
Now the consumer, in maximizing his utility, has two alternatives: (1)
he can take the combination {q1 » 0, q_ = y /p9), or (2) he can consume
(ci.) (ci) i
the set lq, » q} , q,
Based on the theoretical concepts developed up to this point, recreation-
ists will tend to spend fewer days at a site, per visit, as costs of
travel increase. There is, however, a limit as to how high the travel
costs can become, beyond which the consumer will not recreate. In Figure
9, when k « k., the consumer is indifferent between recreating and not
recreating, while if k < k., he prefers to recreate a certain amount,
depending on how much smaller k is than k^ If k > k^ the consumer would
maximize his utility by not recreating, as when k « k . The travel cost
of k » k. will be referred to as the "critical" travel cost, and will be
.,
denoted k*. In this case,
*
for PI = p° (18)
25
-------
Non-
recreation
y -k Recreation (Q )
O 2 1
Figure 9. The Optimal Combinations of Recreation and Non-Recreation
Given Travel Costs of k , k., and k,, for Given Prices p?
Q O 1 L J.
and p_, and Fixed Income y .
26
-------
The effect on the number of days of recreation demanded, per visit, is
zero for decreases in k when:
k - Ak > k*
That is, if the value of k decreases, but the resulting travel cost is
still larger than the critical travel cost, k*, the person will not re-
create. For any decrease in k such that:
k - Ak < k*
the effect on the quantity demanded for recreation will be the same as an
increase in income. The effect on the amount of recreation consumed de-
pends on how much smaller k is than k*, that is, upon the size of (k* - k)
The value of the critical travel cost can be expressed as a function of
four independent variables, k* depends upon on-site costs, the cost of
one unit of q-, the level of income, and the utility function:
k* - k*(Pl, p2, y, U) (19)
As p^ or p2 increase, the value of k* will decrease, due to the fixed
budget available: 3k*/3px < 0, 3k*/3p2 < 0. As the level of income in-
creases, ceteris paribus, so will k*; 3k*/3y > 0, due to the nature of
recreation; that is, it is a normal good. The effect of U on k* will
be discussed later, in conjunction with the utility variable.
The conclusions drawn in this analysis hold for any system of indiffer-
ence curves in which both commodities have positive marginal utilities
and that possess the general shape consistent with maximization of util-
ity, that is, they satisfy the first- and second-order conditions. The
commodities Q, and Q. must be defined in such a way that the indiffer-
ence curves intersect the q_ axis, that is, it must be possible to have
positive utility while consuming no Q..
Changes in On-Site Costs (p.)
Changes in the relative prices of recreation and non-recreation commodi-
ties have a different effect on the demand for recreation, q., than did
the travel cost considered above. A change in either of the prices, p^
or p., will directly affect the optimal budget allocation of the consumer.
The indifference map and budget constraints of an individual, similar to
the one presented in Figure 9, may be analyzed analogously.
By varying the on-site costs, p^ the resulting changes in q^^ can be
observed, and a critical on-site cost, p*, can be defined. The value of
the critical on-site cost depends upon travel costs, the level of income,
the price of other commodities, and the utility function:
Pf - pj(k, 7, P2. u>
27
-------
The effect of k on p. can be illustrated. As k Increases, the critical
price of recreation decreases, 3p./3k < 0. On the other hand, as the
level of income increases, it is expected that the value of the critical
price would also increase, 3p-/3y > 0, due to the fact that recreation is
a normal good. As the price of q. increases, the critical on-site costs
will tend to decrease: 3pj/3p2 < 0.
In general, for given conditions relating to preferences, income, and
prices of other commodities, there exists a critical value of p.^ for every
value of k, and a critical value of k for every value of p..
The model used in this study to determine how many days of recreation will
be taken, per unit of time, can be written in three structural equations:
qL = qi[(k* - k), (p* - PI)] (21)
k* = k*(?1, p2, y, U) (22)
p* - p*(k, y, p2, U) (23)
In Equation (21) it is hypothesized that the quantity of recreation de-
manded per visit will increase as the difference between the travel cost
and the critical travel cost become greater, and as the difference between
on-slte costs and critical on-site costs become greater:
and - - - > 0.
3(k - k)
The empirical specification of this model will be discussed in the next
section. The empirical content of each variable will be specified in
order to determine the statistical model. Sampling procedures are also
discussed.
28
-------
SECTION V
EMPIRICAL SPECIFICATION OF THE MODEL
Some of the variables in the theoretical model cannot be measured directly.
A good example is the utility function of the recreationists. Before the
hypotheses developed in the previous section can be tested, a statistical
model must be developed from the theoretical model. In this section,
empirical implications of each variable in the theoretical model are dis-
cussed .
A general comment should be made before discussing specific variables.
Several of the variables share a common property that cause measurement
problems. The magnitudes of many recreational expenditures increase near-
ly proportionally to increases in the size of the recreational group.
Examples are food, lodging, and other expenses related to individual con-
sumption. To reduce the variation in the variables that is due to the
size of the group, each variable is expressed on an individual basis. The
expenses that a group incurred are divided by the number in the party.
A disadvantage of expressing the cost variables on an individual basis is
that economies of size may be realized when they are not relevant. For
example, automobile expenses remain nearly constant as the size of the
group increases, as long as the number of autos does not increase. How-
ever, the average automobile cost per person would decrease as the size
of the group increases. The low cost-per-person is considered unimportant
in the decision making if the recreational group is a family unit, since
all expenses are paid by the family.
The biases that are forthcoming as a result of expressing the variables on
a per-person basis are not thought to be serious. It is believed that the
economies of size bias are less serious than the biases which would be
introduced by using group observations.
Discussion ofthe Variables
Days of Recreation per Visit (q.)
The questionnaire used for data collection was designed to determine when
the recreationist arrived at the site, and when he planned to leave. From
this information, the number of days the recreationist stayed at the site
can be determined.
Travel Cost Ck)
The travel cost the recreationist incurs to recreate consists of the cost
of transportation, food expenditures, lodging, camping fees, and any other
29
-------
expenses encountered while traveling to or from the recreational site.
Some of these components will be studied separately.
Cost of Transportation; The transportation cost is the
amount it costs the recreationist to drive to and from
the recreational site. This includes gasoline, oil, de-
preciation, insurance, repairs, and any other miscellaneous
items involved with operating an automobile. These costs
were not specified in the questionnaire. The transporta-
tion cost was computed by multiplying the total number of
miles traveled, in both directions, by a cost-per-mile of
five cents. The cost-per-mile figure was determined from
previous studies as well as current research, in which
recreationists were asked to enumerate their transporta-
tion costs [Guedry, 1970, and Stevens, 1966]. Although
none were encountered in the study, other means of trans-
portation can be accommodated in the model.
Food; The recreationist who spends time away from home
must make arrangements for his food consumption. He may
prepare food at home to take with him, or purchase the
ingredients at grocery stores to prepare along the way,
or he may patronize restaurants and cafes. In any case,
the recreationist may end up spending more, less, or the
same amount of money for food while traveling as he would
have spent if he had stayed home.
The relevant food expenditure made by the recreationist
is not the total amount spent for meals while traveling.
The amount that he would have spent at home, had he
chosen not to recreate, should be deducted from his food
expenditures associated with the recreational visit. In-
formation was not collected to determine how much the
recreationist would spend for food while at home. How-
ever, U.S. Department of Agriculture data [1968, Table
2, p. 7] was adjusted to indicate the average daily food
costs per person for various levels df income in 1967.
' The appropriate average expenditure for food at home was
subtracted from the average expenditure per person for
food while traveling. The difference, which, in some
instances was negative, was added to the calculations
of the travel cost variable. If no expenditure was made
for meals while enroute, this adjustment was not made.
Other Costs of Travel; The cost of lodging, camping
fees, and any miscellaneous expenses while traveling
were obtained in the personal interview.
On-Site Costs (p.)
f
On-site costs are the total costs incurred by the recreationist per day
while visiting the recreational site. They include the costs of lodging,
30
-------
camping fees, equipment rentals, meals, and other miscellaneous expenses
incurred at the site. The total expenses that the recreational group
incurred per day are divided by the number of persons in the group to
obtain the daily on-site cost per person.
The daily food cost per person, while recreating at the site, is computed
from information obtained in the interview. For reasons mentioned above,
the average daily expenditure per person for food while at home, within
the corresponding income groups, is subtracted from the calculated on-site
food cost per person per day. The difference in the two figures, whether
positive or negative, is used in the calculations to determine the p.
variable. All of the remaining components of the on-site cost variable
are accounted for in the questionnaire.
j
!
Income (y)
In this analysis the family income of the recreationist, after taxes, is
used. The questionnaire was used to obtain data about the size of the
recreationist's family, the age of the household head, and the gross
family income. It was then possible, using a Federal Income Tax table,
to estimate the amount of federal taxes paid in 1967. It was not feas-
ible to estimate the amount of state taxes paid, since recreationists
came to Oregon's lakes from several states. Thus, the income used in
this analysis is biased upward. However, the error is not considered
significant. Federal income taxes are usually much larger than state
taxes. The majority of the relevant taxes have been subtracted.
)
Price of Other Commodities (p.)
The price of other commodities, in theory, is equal to the weighted aver-
age of the prices of all other commodities that the consumer may choose
to purchase:
P2 = V3 + V4 + +«n-2*n
where p. is the price of the i commodity, and a is the weighting fac-
tor of the i commodity. In practice, however, the commodities that
comprise the alternatives to recreation are so numerous and so diverse
among individuals that it is impossible to specify them. Therefore, the
P2 variable was deleted from the statistical model.
Utility (U)
The utility variable in Equations (22) and (23) is important in deter-
mining the critical values of travel cost and on-site costs. A change
in the shape of the indifference curves, through a change in the utility
^t ^t
function, will cause a change in k and p.. Unfortunately, the utility
function is not measureable. However, it can be represented, in part, by
several other variables. Some of the variables considered important in
this respect are the characteristics of the recreationist, jthe character-
istics of the site, and the value of recreational equipment.
31
-------
Characteristics of the Recreationist; The recreation-
ist's characteristics influence his decisions concern-
ing the consumption of recreation. The background of
the person, his stage in the family cycle, his age, and
so on, influence his utility function. However, with
the exception of income, these personal characteristics
of recreationists were not taken into account in this
study. In another study conducted at Oregon State Uni-
versity, Guedry [1970] specified the relationship be-
tween the characteristics of the individual recreation-
ist and the demand for recreation.
Site Characteristics; Recreationists choose a site be-
cause of the "desirability" of its characteristics. If
a study is conducted to determine the recreational use
and value of a particular site, and information is gath-
ered only at that site, the characteristics of the site
are fixed and do not need to be analyzed explicitly. How-
ever, if data are collected at more than one site, and
each of the sites has different characteristics, the char-
acteristics may explain the variation in quantity of recrea-
tion days observed at the sites, and the characteris-
tics that are desirable to recreationists could be iden-
tified. Determination of the characteristics that have
a substantial effect upon the use and value of the site
can help decision makers plan site alterations to gain
the user benefits from favorable characteristics.
The specific site characteristics of interest in this
study are the size of the lake (measured in acres),
and the level of use of each lake for various recrea-
tional activities. The activities considered are swim-
ming, boating, water skiing, fishing, and camping. Dis-
crete values were used to indicate the amount each of
the lakes was used for each activity. If an activity
was non-existent at a lake, it was given the value of
zero. Low, medium, and high uses of the lake for a given
activity were assigned the values one, two, and three,
respectively. The use-intensities were estimated by U.S.
Forest Service personnel and employees of the E.P.A. who
were knowledgeable about the lakes' characteristics.
It is recognized that the values are subjective. Table
1 contains the estimated use-intensities for each activ-
ity at each lake in the study area. The selection of
the four lakes used in the study will be discussed later
in this section.
Investment in Recreational Equipment; It is hypothesized
that the value of recreational equipment owned by the
individual may serve as a proxy for a person's utility
function with respect to recreation. An individual with
32
-------
Table 1. Estimated Use-Intensities for Certain Recreational
Activities and Lake Size, by Lake
CO
Use- Intensities
Lake
Lake of the Woods ....
Odell
Willow
Swimming
3
0
1
0
Water
skiing
3
0
1
1
Boating
3
1
1
1
Fishing
1
3
3
1
Camping ,
picnicking
3
2
2
0
Lake
size
(acres)
1,055
3,500
320
98.560
-------
a large quantity of recreational equipment, such as boats,
campers, trailers, and so forth, probably has a stronger
preference for recreation than a person with less equip-
ment. A qualification is necessary, however. This pheno-
menon would be expected to be observed only when a compari-
son is made among similar activities. Wilderness-type activ
ities cannot be compared to those at a more accessible site,
since each requires a unique combination of equipment.
Investment in recreational equipment may also be a useful
substitute for income as an explanatory variable. Two rea-
sons seem apparent. First, investment is more correlated
with the permanent income of the recreationist than with
current annual income. This is important, since permanent
income is considered more closely associated with the quan-
tity of recreation taken than is current income. A case
in point is a retired person. He may have a low current
income, but the amount of equipment he owns is related to
his previous permanent income. On the other hand, a young
person beginning his career probably purchases equipment
with the future in mind. Even though he may have a low
current income, it may be his expected permanent income
that determines his purchases of equipment.
There is another closely related reason why the amount of
recreational equipment may be more useful as an explanatory
variable than is current income. While the recreationist*s
income stream may be stable over time, his expenditures
for items other than recreation may fluctuate widely. These
fluctuations may be due to the "lumpiness" of certain house-
hold expenditures, as well as to the occurrence of events
in a person's life which necessitate unusually high expendi-
tures during a given period for which no plans had been
made. Cash outlays for outdoor recreation during any one
period may be subject to these fluctuations in expendi-
tures for other commodities. On the other hand, the con-
sumer's investment in outdoor recreational equipment may
reflect more nearly his long-run budgeting plans.
^
The Statistical Model
The statistical model, when more than one site is analyzed, is:
qi= qi[(k ~k)> (pi" V1 for (k ~k)> (p* ~ pi) - °
k = k (p^ y, Sw, Ws, B, F, C, I, Si) (25)
* ' *, '
pl = pl*k» y> Sw' Ws> B» F> C> I) Si) (26)
where Sw, Ws, B, F, and.C represent the site's use-intensity for swim-
ming, water skiing, boating, fishing, and camping, respectively, i
34
-------
indicates the value of recreational equipment and Si indicates the size
of the lake, in acres. All other variables are as defined above.
The demand function of interest in the study is the aggregate demand
function for the total number of visitor-days per season. The preceding
model is appropriate for explaining the number of visitor-days per visit.
That is, it pertains to an individual, not to the population of users.
The total number of visitor-days can be obtained by multiplying Equation
(24) by the estimated number of visits (V) to the site during the season.
The appropriate aggregate model is:
Vq-L =* f[(k* - k), (p* - PI)] for (k* - k), (p* - PI) > 0 (27)
k* = k*(pr y, Sw, Ws, B, F, C, I, Si) (28)
p* = p*(k, y, Sw, Ws, B, F, C, I, Si) (29)
where V indicates the number of visits to the site during the season.
The total number of visits at each site during the relevant season was
obtained from the U.S. Forest Service, since the lakes studied had facili-
ties maintained by the Forest Service.
The Number of Visits Relationship
One other relationship must be discussed. The aggregate demand model
contains the V variable, which represents the number of visits to the
site. This variable can be estimated in two possible ways.
The first approach is to use the estimates of the number of visits re-
ported by the U.S. Forest Service, and have it remain fixed with respect
to any changes in the independent variables in the model. The second
method is to use the estimated number of visits, as above, but then ex-
press V as a function of some appropriate explanatory variables. In this
way, when a postulated change occurs in the independent variables, the
effect upon the number of visits, as well as upon the length of stay per
visit, can be observed. The second approach gives a more meaningful
estimate of the total number of visitor-days.
In line with the second approach, it is hypothesized that the number of
visits forthcoming at a site for an individual can be expressed as a
function of the travel cost, the income of the recreationist, and the
characteristics of the site. Information was not obtained from recrea-
tionists to determine the number of visits they would make during the
season. Thus, it is impossible to focus attention on the individual
recreationist. An alternative does exist, however. The total estimated
visits, V, can be allocated to regional population groups, and the re-
lationship between the number of visits from the i region and the ex-
planatory variables can be computed. It is hypothesized that the number
of visits forthcoming from an area, V, is functionally related to the
average travel cost, k, of recreationists residing in the area, the
35
-------
the average income of recreationists from the area, y, the total number
of persons living in the area, pop, and the characteristics of the site
under consideration:
V - V(k, y, pop, Sw, Ws, B, F, C, Si) (30)
Sampling Procedures
To estimate the statistical demand model, primary data had to be gathered
from recreationists. Since the primary objective of the study is to
estimate the recreational use of Klamath Lake with improved water qual-
ity, it is necessary to collect the data at lakes that have different
characteristics. By observing the various characteristics of these
lakes and the intensity of each lake's use, it is possible to predict
the increase in use of Klamath Lake as its characteristics, such as
water quality, improve.
Three lakes, in addition to Klamath Lake, were chosen for the data col-
lection process. They are Odell Lake, Lake of the Woods, and Willow
Lake. These lakes were chosen for several reasons. First, many of the
recreationists living in the Klamath Falls area are now using the three
lakes, or other lakes in the vicinity of these lakes, for recreation.
Also, these lakes possess many of the characteristics, such as the size
and the water recreation activities, that are of interest in this study.
Only lakes that were easily accessible and had overnight facilities were
considered, since these attributes were deemed a necessity for the aver-
age recreationist to consider substituting that lake for Klamath Lake.
For sampling purposes the population was defined as the total number of
recreationists that visited the four lakes during 1968. The sampling
unit is the recreation unit; that is, the group that recreates together.
The appropriate sampling frame would be a list of all the recreation
units found in the area of study in 1968. Of course, such a listing is
impossible to obtain. Therefore, stratified random sampling techniques
were used to obtain the sample.
First, standard statistical methods were used to estimate the sample
size necessary to obtain the precision desired for the study. A sample
size of 300 was estimated. A complete discussion of the estimation of
the sample size is contained in Gibbs [1969].
The total sample of 300 was then allocated to the four lakes on the basis
of the estimated number of recreation days taken at each lake. Data
available from the U.S. Forest Service and other agencies provided esti-
mates of the number of recreation-days taken at each of the four lakes
in 1967. These were summed to obtain the total number of recreation-
days taken at all four lakes. If a lake accounted for 30 percent of the
total recreation-days, 30 percent of the sample size of 300 was allocated
to that lake, and so forth.
36
-------
The area immediately surrounding each lake was also divided into several
geographic blocks. For example, all camping areas, boat ramps, picnic
areas, lodges, cabins, etc., were placed in separate blocks. The sample
size allocated to each lake was again distributed to the various geo-
graphic blocks on the basis of frequency-of-use of each of the blocks.
The same procedure was used at each of the four lakes.
The proper time to conduct the interviews also had to be determined. To
accomplish this, all possible weeks in the summer season were numbered,
and two weeks were chosen randomly. The total number of interviews needed
at each block at each lake was divided equally between the two weeks.
Estimates were then obtained from the appropriate agencies as to the rel-
ative use of the lakes during the week and weekends. The sample was then
allocated by this factor. If twice as many people recreated on weekends
as during the week, two-thirds of the sample data were collected on the
weekend. Table 2 shows the final distribution of the sample among the
sites, weeks and days for each lake.
The recreationists within each block at each lake were then selected at
random to be interviewed. Care was taken that the sample was representa-
tive of the activities at the site. That is, if approximately two-thirds
of the people at a site were picnicking, and one-third were water skiing,
the sample contained twice as many picnickers as water skiiers. Care
was also taken to prevent interviewing recreationists on the basis of the
type or amount of equipment they were using. The questionnaire used in
the study is included in Appendix A.
37
-------
Table 2. Number of Interviews Taken at Each Lake, by
Block, for the Four Time Periods.
First Week
Second Week
Lake
Block
Week
days
Week
end
Total
Week
days
Week
end
Total
Two-week
total
WILLOW:
KLAMATH: Recreation Creek 1 2
Odessa. 0 1
Rocky Point Resort 3 11
Moore Park 2 7
Pelican Marina 0 1
Yacht Club 0 1
Public Boat Launch
& Bank Fishermen 0 0
TOTAL KLAMATH LAKE 6 23
LAKE OF THE WOODS: Rainbow Bay 5 17
Aspen Point 3 13
White Pine 0 2
Lake of the Woods
Resort 3 11
TOTAL LAKE OF THE WOODS 11 43
ODELL: Princess Creek 6 7
Sunset Cove 3 3
Trapper Creek.r........ 10 11
Pebble Bay 0 0
Odell Creek.... 1 2
Odell Summit Lodge 1 2
Odell Lake Resort 1 1
Shelter Cove Marina.... 0 1
TOTAL ODELL LAKE 22 27
County Campground...... 5 16
TOTAL 44 109
3
1
14
9
1
1
0
^tn^ivgak^
29
22
16
2
14
54
13
6
21
0
3
3
2
1
(^VO^
49
21
153
1
0
3
2
0
0
0
mmillitimm
6
5
3
0
11
6
2
11
0
1
1
1
0
M^Mtov
22
44
2
0
11
6
1
1
1
HH
22
17
12
2
10
^M^MHUVI
41
7
3
10
0
1
1
1
1
^^^v
24
16
103
46
21
147
42
300
CO
-------
SECTION VI
ESTIMATING AND APPLYING THE STATISTICAL DEMAND MODEL
The data collected from recreationists at the four lakes in the study
area are used to estimate the equations of the hypothesized statistical
demand model. Four relationships are estimated. They are: p* the
critical on-site cost relationship; k*, the critical travel cost
tionship; q , the demand relationship; and V, the number of visits
relationship.
Before each of the relationships are discussed, a problem which was en-^
countered in three of the equations will be discussed. When the equa-
tions for critical travel cost, critical on-site cost, and the number
of visits were estimated, multicollinearity was observed among the site
characteristic variables of swimming, water skiing, and boating use-
intensities. When one of the three use-intensity variables entered int;p
the regression equation, neither of the other two variables could explain
enough additional variation in the dependent variable to be significant.
Since the simple correlation coefficients between the three variables
ranged from .957 to .980, it was not possible to estimate the separate
influence of each of the three variables. Consequently, the three vari-r
ables were combined into one variable. The use-intensity rankings for
swimming, water skiing, and boating were summed to represent a single
variable for each lake, denoted as W.
Another case of multicollinearity was observed between the camping in-
tensity variable and income. This was considered to be a statistical
problem with no economic significance. Because of their differing na-
ture, it was not feasible to combine the two variables. Instead, the .
camping intensity variable was deleted from the model, since camping inr
tensity may be more closely related to the man-made characteristics of
the site than the natural characteristics being considered in this study.
Statistical problems also prevent the use of the recreational equipment
variable (I) in the study. The problems can be illustrated by discuss-*
ing the work of Guedry [1970]. In his equation to determine the number
of recreation days taken, per capita, in the Bend Ranger District in
Oregon, the "investment in recreational equipment" variable was signifi^-
cant at the 2 percent level. However, the sign of the coefficient was
negative. The negative sign is somewhat confusing, since it suggests
that the average length of stay at the recreational site decreases as
the amount of investment in recreational equipment increases. This is
opposite from the effect that one would expect. To determine a reason
for this, all variables in the equation that had a simple correlation
coefficient greater than or equal to .7 with the recreational equipment
variable were removed, and a new equation was estimated. The new par-
tial regression coefficient for the equipment variable in the new equa-
tion was significant only at the 50 percent level.
39
-------
In a further attempt to clarify the problem, Guedry removed all variables
with a simple correlation coefficient greater than or equal to .6 with
the equipment variable. A new equation was then estimated, and the par-
tial regression coefficient of the recreational equipment variable was
significant at the 10 percent level, and the sign of the coefficient was
positive. The erratic performance of the recreational equipment variable
makes it difficult to form any conclusions as to its role in the demand
equation. Since the same type of problems were experienced in this study,
investment in recreational equipment is omitted as an explanatory vari-
able. The variable appears to be too highly correlated with other vari-
ables in the model to be of significant value.
The above changes leave the statistical model to be estimated as:
q;L - q]L[(k* - k), (p* r PL)1 for (k* - k) and (p* - PI> >, 0 (31) .
p* - p*(k, y, W, F, Si) (32)
k* = k*(pr y, W, F, Si) (33)
V = V(k, y, pop, W, F, Si) (34)
Each relationship will be discussed below.
Critical On-Site Cost Relationship
Critical on-site cost is related to travel cost, level of income, and
site characteristics. Since the estimation procedure is performed on
more than one recreational site, the observations were categorized by
sites, and placed in homogeneous groups determined by income level and
travel costs. The income groups were determined as follows: the in-
comes of all recreationists were listed in descending order of magnitude.
Consideration was given to the "natural" breaks in the list; but, due
to the small number of observations, only two cutoff points were chosen.
The cutoff points were chosen to ensure that each group would have
approximately the same number of observations. For all lakes, the three
income groups are: (1) less than or equal to $8,000, (2) between $8,000
and $10,000, and (3) greater than or equal to $10,000.
The distribution of travel costs is different for each lake. For this
reason the groups were determined individually for each lake. The cut-
off points for Klamath Lake are $1 and $19. That is, the three groups
are: (1) less than or equal to $1, (2) between $1 and $19, and (3)
greater than or equal to $19. For Lake of the Woods, the cutoff points
for k are $2 and $20; for Odell Lake, $5 and $10; and for Willow Lake,
$2 and $10.
To estimate the maximum PI within each subgroup, determined by income
and travel costs, the variable on-site costs in each subgroup were ar-
ranged in ascending order of magnitude. The last (or n ) p.. is the
40
-------
maximum p. observed in the subgroup, and is referred to as the nth order
4*^t
statistic. The n order statistic is used as a reliable estimate of the
maximum p in the distribution [Hogg and Craig, 1965, ch. 6], The use
L* j^
of the maximum observed p^ as an estimator of p. does not imply that all
other p^'s are ignored. The maximum p- is chosen only after it has been
compared to all other p's in the subgroup. Thus, all the sample informa-
tion is used.
As a result of the above classification technique, the number of observa-
tions varies in each subgroup. The reliability of the estimate of p..
depends upon the number of observations in the subgroup. Reliability
refers to the size of the variance. If the variance is large, the esti-
mator is less reliable. In utilizing regression analysis, it is assumed
that the diagonal elements in the variance-covariance matrix are con-
.'j.... , ^
stant, or nearly so. In this case, the p's of some subgroups have
higher variances than others; thus, the constancy of variances assump-
tion is violated. The coefficients estimated by ignoring this type of
problem will'be unbiased,, but will not have minimum variances. It is
necessary,'then, to make adjustments in the analysis to ensure unbiased,
minimum variance estimators. Weighted least squares was used to correct
the problem. The technique involves assigning larger weights to the
reliable estimates than to the unreliable ones [Draper and Smith, 1966].
The weights are equal to the square root of the number of observations
in the subgroup.
The level of income and the travel cost, from each subgroup, are used as
observations and are then regressed on the resulting p, *s (for each sub-
group) to obtain an estimate of the relationship between the independent
variables and p?. The critical on-site cost relationship estimated by
weighted least squares is:
p* = -7.263 + 7.80 W### + 2.630 F### + .000067 Si#// - .004 k2#
1 (.197) (.815) (.000025) (.002)
* ")& ") ftiHt (35)
+ .269 k + .000000017 y V R - .684*
(.143) (.0000000094) Degrees of freedom =27
where W, F, and Si are the site characteristic variables, as previously de-
fined, k is the average travel cost of the subgroup, and y is the aver-
age income for the subgroup. The standard error of the coefficients is
shown in parentheses below the coefficients. Each coefficient was tested
to determine if it was significantly different from zero. The test is
made by dividing the coefficient by its standard error and comparing the
resulting value with the values in a student's t table. A 1 percent
level of significance is referred to by ###, a 5 percent level of signi-
ficance by ##, and # indicates the coefficient is significant at the 10
percent level. If no marks are listed, the coefficient is sufficiently
different from zero at a level of probability greater than 10 percent.
41
-------
Only two variables, W, and F, are significantly different from zero at
the 1 percent level. The size of the lake variable is significant at
the 5 percent level, while travel cost, travel cost squared, and income
squared are all significant at the 10 percent level.
It was hypothesized that the site characteristics should have a positive
effect on the critical on-site costs. The obtained results are consis-
tent with this hypothesis. The conceptual framework of this study also
suggested a negative relationship between travel cost and critical on-
site costs. Equation (35), however, indicates that the relationship is
positive. The analysis suggests that as travel costs increase, the crit-
ical on-site costs will also increase, but at a decreasing rate, since
the k-coefficient is positive but the k coefficient is negative.
*
Income has, as was hypothesized, a positive influence on p.^. The relia-
bility of this relationship is not high, since the coefficient is signi-
ficant only at the 10 percent level. The evidence indicates, however,
that as income increases, the critical on-site costs will increase at an
increasing rate. The difficulties of defining and obtaining data for.the
appropriate income variable were discussed earlier. Perhaps these ex-
plain the failure of the empirical model to produce a statistically'more
significant result with respect to the income variable.
2
The R for the critical on-site cost equation is .684, which is signi-
ficant at the 1 percent level.
From the estimated equation it is possible to see the predicted effect
on p, of changing the characteristics of the site. For example, if fish-
ing intensity were to increase one unit, perhaps due to a change in the
water quality, the recreationist would be willing to increase the maxi-
mum willingness to pay at the site by $2.63 per day.
Critical Travel Cost Relationship
The critical travel costs, k fs, were also estimated by using the n
order statistic after the observations had been separated into subgroups
on the basis of lakes, income, and on-site costs. The income groups are
the same as those used in the critical on-site cost relationship, while
the subgroups defined by p.., for all lakes, are: (1) < $1.50, (2) be-
tween $1.50 and $2.50, and (3) >_ $2.50. Average values" of income and
on-site costs were determined for each group. The predicted k* equation
is:
k* - -36.711 + 6.248 W * + 3.779 F + .0003 Si + .0020 y
(2.322) (7.800) (.0002) (.0018)
+ 10.435 p/## R2 . .616*" (36>
(3.349) Degrees of freedom - 28
In Equation (36) only the on-site costs variable is significant at the
1 percent level, while the "water" variable, W, is significant at the
42
-------
5 percent level. All other variables fail to obtain the 10 percent level
of significance.
It was hypothesized that the characteristics of the site have a positive
effect on k . That is, as the characteristics of the site improved, re-
creationists would be willing to pay more in travel costs. The sample
data supports this hypothesis, since the W, F, and Si variables are all
positive. However, due to the low significance of the fishing intensity
and the lake size variables, few conclusions can be stated with much re-
liability concerning the existence of a relationship between these vari-
ables and k*.
The sample data also suggests a positive relationship between income and
critical travel costs. This had been hypothesized. Again, however, the
low level of significance of the income coefficient makes it impossible
to place much reliability upon the relationship.
The'lack of significance of the income variable may be due, in part, to
the broad income groups used to estimate k*. Since only three income
groups were used, the income range within each group was quite large.
More data would have made it possible to define smaller ranges of income.
Then the variation in income, and its effect upon k*, could have been
more clearly observed.
On-site costs, statistically the most significant variable in the equa-
tion, exhibits a positive relationship with k . However, the theory sug-
gested that as a person was required to spend more at a recreational
site, he would be willing to pay less in travel costs, due to his fixed
budget. This hypothesis is rejected by the sample data. Possible ex-
planations may include the fact that on-site costs usually comprise a
much smaller portion of the recreationist's budget than do travel costs.
Because of this, other effects may be more important in the decision-
making. For example, in this study the more desirable sites may have a
higher daily on-site cost. Recreationists may be willing to pay higher
travel costs to visit the more desirable site, even if on-site costs are
slightly higher.
The coefficient of determination, R , for the k equation, is .616. It
is significantly different from zero at the 1 percent level.
Days Per Visit Relationship
* *
The above discussion refers to the estimation of the k and p^ values.
Each questionnaire contains data that made it possible to compute the
length of stay per visit, q-, the actual travel cost, k, and the actual
on-site cost, p,. Therefore, the independent variables for the q1 equa-
tion, (p? - p,) and (k* - k), are obtained by subtracting the observed
1 i ju A
p.. and k values from the appropriate group's p.. and k values.
43
-------
Since 304 observations were collected, there are 304 possible sets of
values of (p? - p,) and (k* - k) to use in the regression equation. How-
,ever, two distinct groups of recreationists were observed in the sample.
One group was characterized by spending less than three weeks at the site
and having relatively high values of (p* - p.^. The other (much smaller)
group spent a longer time at the site (up to 169 days) and had relatively
low values of (p* - p..). This group included retired people spending
most of the season at the site, and persons such as teachers, who did
not have summer job commitments.
Further analysis of the recreationists in the second group revealed that
they did not respond significantly to changes in p1 and k. That is^ there
was no relationship between the length of stay per visit and the (p. - p^)
and (k* - k) variables. Therefore, the group of recreationists that
stayed at the site 20 days or more was not used to estimate the q^ equa-
tion. The remaining 282 observations were used to estimate the follow-
ing q.. relationship:
Inq- = .759 - .0064 (k* - k)*** + .0637 (p* - p.)*** (37)
1 (.0018) (.0189) L
R2 = .113***
Degrees of freedom =279
The average length of stay per visit for recreationists in this group is
3.4 days.
It was hypothesized that as the difference between the critical travel
cost and the actual travel cost increased, the number of days the recrea-
tionist would remain at the site per visit would also increase. In
Equation (37) a negative coefficient is estimated which is significant
at the 1 percent level. In other words, evidence suggests that, for a
given critical travel cost, as a person's actual travel costs increase,
he will tend to recreate more days per visit. As was mentioned earlier,
the appropriate income in the budget constraint depicted in the theory
is (y - k). As k increases, less income is available to be spent at the
site after arrival - thus fewer days will be forthcoming. Apparently
travel costs are so small, relative to income, that they do not signi-
ficantly reduce the income available for expenses at the site.
It was also hypothesized that as the daily on-site costs increased,
given a fixed p^, fewer days per visit would be observed. This hypothesis
is substantiated by the analysis. The (p* - p ) variable is significant
at the 1 percent level.
2
The R for Equation (37) is .113, which is significant at the 1 percent
level. The R is low; yet it must be remembered that in contrast to
the previous equations, the number of observations is very large.
44
-------
The Number of Visits Relationship
Counties were used to represent the regions in the visits equation dis-
cussed earlier. Information in the questionnaire indicates the county
in which the recreationists resided. Record was made of the number of
recreationists that originated from each county. These were expressed
as a percent of the total sample compiled at each lake, and then multi-
plied by the estimated total visits for the season to estimate the number
of visits from each county for the season.
The travel cost and income of all persons in the sample from each county
had to be averaged to obtain average values for the regions. The popula-
tion of each county was determined from the U.S. Bureau of the Census
Population Estimates, 1966. The relevant counties, the population of
the counties, as well as the information on visits, travel cost, and
income, are listed in Table 3. Each lake is listed separately. It
should be noted that the recreationists in the sample came from only
four states: Oregon, California, Nevada, and Idaho. The sampled lakes
are not well known outside the State of Oregon.
'i
All of the data collected at the four lakes are used to estimate the
visits relationship. For each of the counties observed at Klamath Lake,
for example, the values assigned to the characteristics of Klamath Lake
are used, along with the values of the other independent variables for
that county group. There are data from 12 counties for Klamath Lake,
27 counties for Lake of the Woods, 29 for Odell Lake, and 9 for Willow
Lake. Thus, 77 observations are available.
Since the independent variables k and y were aggregated within each
county, some were more reliable than others, due to the number of obser-
vations within each county. Weighted least squares, similar to that
JU JL
discussed for determining the p., and k relationships, was used to cor-
rect this problem. The estimated visits equation is:
-67,947.046 + 7,312.442 W" + 21,024.198 F1M"r (38)
(842.177) (2,366.595)
-I- .648 Si*" - 149.953 k - .118 y - .003 pop"
(.068) (167.595) (.824) (.0019)
R2 = .874*"
Degree of freedom * 70.
The site characteristics, referred to by W, F, and Si, are as defined
earlier; k refers to the average travel cost of recreationists from each
county; y represents the average income of recreationists from each
county; and pop refers to the total population of each county.
It should be noted that the visits equation is redundant if one is not
interested in changing some of the independent variables and predicting
a change in total visitor-days. That is, if no changes are considered,
45
-------
Table 3. The Population, Number of Sample Visits, Percent of Sample Visits,
Visits per Season, Travel Cost, and Income, by County, for each
of the Four Lakes
KLAMATH LAKE
County
Population
of county
(pop)
Sample
visits
Percent of
sample from
each county
Visits
(V)
Average
travel
cost
(k)
Average
income
(y)
Oregon:
Deschutes 27,600 1
Jackson 91,300 5
Josephine 37,000 2
Klamath 49,600 29
Lane 200,700 1
£ Multnomah 534,900 2
Washington 126,100 1
California.:
Orange 1,171,400 1
Los Angeles 6,814,500 3
San Bernardino 628,900 1
Santa Clara 929,800 1
Trinity 8,200 1
TOTAL 48
2.1
10.4
4.2
60.4
2.1
4.2
2.1
2.1
6.3
2.1
2.1
2.1
100.2
3,070
15,205
6,140
88,305
3,070
6,140
3,070
3,070
9,211
3,070
3,070
3.070
146,491
(dollars)
4.67
2.16
3.83
0.26
4.70
51.33
80.32
28.63
80.26
119.39
19.29
63.17
(dollars)
18,372
7,547
10,329
8,385
3,956
5,342
3,860
13,440
13,355
5,228
15,315
7,414
Continued
-------
Table 3. (Continued)
LAKE OF THE WOODS
County
Population
of county
(pop)
Sample
visits
Percent of
sample from
each county
Visits
(V)
Average
travel
cost
(k)
Average
income
(y)
Oregon;
Coos 54,100 1
Des chutes 27,600 1
Douglas 72,600 2
Jackson 91,300 46
Josephine 37,000 6
Klamath 49,600 19
Lane 200,700 2
Lincoln 25,500 1
Linn 65,600 2
Multnomah 534,900 2
California;
San Francisco 714,600 2
Monterey 229,900 3
Contra Costa 514,400 1
Orange 1,171,400 3
Alameda 1,030,400 4
Los Angeles 6,814,500 10
Humboldt 101,300 1
Santa Barbara 253,400 1
Siskiyou 35,000 3
San Mateo 519,100 1
San Bernardino 628,900 1
Santa Clara 929,800 9
San Joaquin.... 283,500 1
Sacramento 597,700 2
Del Norte 16,700 1
.8
.8
1.6
36.2
4.7
15.0
1.6
.8
1.6
1.6
1.6
2.4
.8
2.4
3.1
7.9
.8
.8
2.4
.8
.8
7.1
.8
1.6
2,130
2,130
4,260
96,388
12,515
39,940
4,260
2,130
4,260
4,260
4.260
6,390
2,130
6,390
8,254
21,035
2,130
2,130
6,390
2,130
2,130
18,905
2,130
4,260
2,130
(dollars)
14.36
9.17
11.51
1.80
.78
2.84
8.66
91.30
9.96
4.58
58.63
50.86
79.38
33.85
36.71
54.78
6.48
19.20
3.92
17.01
26.76
28.92
35.28
26.20
9.10
Continued
(dollars)
7,528
12,048
7,131
10,471
10,589
8,327
10,335
10,746
11,850
12,506
13,106
7,057
13,740
10,790
15,570
14,942
10,215
5,646
11,893
11,010
13,440
15,412
11,010
6,492
7,414
-------
Table 3. (Continued)
LAKE OF THE WOODS
County
Nevada :
Clark
Idaho:
TOTAL
Population
of county
(pop)
233,700
60,400
Sample
visits
1
1
127
Percent of
sample from
each county
.8
.8
100.4
(Continued)
Visits
(V)
2,130
2,130
267.327
Average
travel
cost
(k)
(dollars)
46.22
8.68
Average
income
(y)
(dollars)
13,590
10,620
oo
Continued
-------
Table 3. (Continued)
ODELL LAKE
County
Population
of county
(pop)
Sample
visits
Percent of
sample from
each county
Visits
(V)
Average
travel
cost
(k)
Average
income
(y)
Oregon;
Benton 49,100 3
Clackamas 146,100 4
Coos 54,100 2
Crook 10,100 1
Des chutes 27,600 2
Douglas... 72,600 2
Jackson 91,300 3
Klamath 49,600 4
Lane 200,700 30
Lincoln 25,500 3
S Linn 65,600 1
Marion 141,700 5
Multnomah 534,900 7
Polk 30,900 2
Washington 126,100 4
California;
Contra Costa 514,400 2
Orange 1,171,400 1
Alameda 1,030,400 2
Los Angeles 6,814,500 6
Shasta 75,500 1
Siskiyou 35,000 1
San Mateo 519,100 1
Santa Clara 929,800 3
Modoc 7,500 1
Kern 325,200 1
3.1
4.1
2.1
1.0
2.1
2.1
3.1
4.1
30.9
3.1
1.0
5.2
7.2
2.1
4.1
2.1
1.0
2.1
6.2
.0
.0
1.
1.
1.0
3.1
1.0
1.0
5,595
7,400
3,790
1,805
3,790
3,790
5,595
7,400
55,769
5,595
1,805
9,385
12,995
3,790
7,400
3,790
1,805
3,790
11,190
1,805
1,805
1,805
5,595
1,805
1,805
(dollars)
6.45
7.22
11.29
3.87
12.14
2.40
8.17
2.32
4.66
6.45
,00
.67
,86
10.58
11.77
5,
7.
9,
23.11
44.53
44.04
28.79
12.37
15.09
12.87
29.44
10.05
24.97
(dollars)
8,318
5,259
5,280
7,414
5,373
7,748
11,194 ,
6,822
7,256
11,804
8,472
6,688
11,747
9,005
12,567
8,669
18,540
6,940
15,502
11,784
7,114
12,048
11,826
9,519
10,746
Continued
-------
Table 3. (Continued)
County
California (Continued) :
Marin
TOTAL
Population
of county
(pop)
188,600
1.188.000
283,500
193,700
Sample
visits
1
2
1
1
97
ODELL LAKE
Percent of
sample from
each county
1.0
2.1
1.0
1.0
99.8
(Continued)
Visits
(V)
1,805
3.790
1,805
1,805
180 , 304
Average
travel
cost
(k)
(dollars)
11.72
40.36
8.39
26.59
Average
income
(y)
(dollars)
21,804
8.330
15,615
1,750
o
in
Continued
-------
Table 3. (Continued)
WILLOW LAKE
County
Population
of county
(pop)
Sample
visits
Percent of
sample from
each county
Visits
(V)
Average
travel
cost
(k)
Average
income
(y)
Oregon;
Douglas 72,600 1
Jackson 91,300 17
Josephine 37,000 3
Klamath 49,600 1
i- Lane 200,700 1
Lincoln 25,500 1
Marion 141,700 1
California:
Los Angeles 6,814,500 5
Siskiyou 35,000 2
TOTAL 32
3.1
53.1
9.4
3.1
3.1
3.1
3.1
99.9
3,397
58,187
10,301
3,397
3,397
3,397
3,397
17,094
6,904
109,471
(dollars)
2.77
1.90
1.94
2.30
8.65
28.53
14.53
78.60
9.83
(dollars)
6,700
8,127
9,589
8,586
7,870
10,614
1,750
6,299
3,580
-------
Equation (38) would merely predict the total number of visits to the site,
which is the information from which the equation was derived. However, in
this study the main interest lies in predicting the results of a change in
the existing situation resulting from a change in water quality on the
number of visitor-days. Here the relationship is important because "visi-
tor-days" is made up of two components - the number of visits, and the
length of stay per visit. Without this equation, only the length of stay
per visit would have been considered.
It should be noted that the population variable in the visits relationship
is not a population of recreationists but, instead, the population of a
county.
Many of the relationships that were hypothesized earlier are substantiated
by the sample data. The positive coefficients of the site-characteristic
variables indicate that the number of visits from a given county will in-
crease as the characteristics improve. Also, the negative coefficient for
travel cost indicates that the number of visits from a county decrease as
the travel costs increase. These reactions were hypothesized.
However, two statistical problems were encountered in Equation (38). First,
the population and travel cost variables are highly correlated. The simple
correlation coefficient between the variables is .711. This relationship
is easily explained. The counties near the recreation sites have a lower
average travel cost than those counties farther away from the sites. Also,
those counties close to' the site have smaller populations than those far-
ther away. Therefore, the population figure increases as the value of k
increases. Johnston and Pankey [1968] observed the same phenomenon in
their study.
Although the correlation between travel costs and population is easily
explained, it creates difficulties. The interrelationship causes each of
the variables to be relatively insignificant in the estimated equation.
The population variable is significant only at the 10 percent level, while
the k variable is not significant at the 10 percent level.
The other problem encountered in Equation (38) is a high level of corre-
lation (.694) between the W variable and income. Once the W variable
enters into the equation, the entry of the income variable fails to reduce
significantly the variation in V. It is believed that the high correla-
tion is the cause for the low significance levels of the coefficients and
the negative coefficient estimated for income. The*"negative coefficient
for income indicates that the number of visits from a county will decrease
as average county income increases. This is not the type of relationship
that was hypothesized.
/
To solve the two statistical problems, a new visits equation was estimated
with the income and population variables deleted, since they did not ex-
plain much of the variation in the previous equation. The new equation
is:
52
-------
V - -71,166.121 + 7,141.764 Wffffff + 19,825.384 r" (39)
(460.199) (1,651.425)
+ .641 Siff* - 379.786 k###
(.059) (115.473) R2 = .868*"
Degrees of freedom = 72.
All variables in Equation (39), including the travel cost variable, are
significant at the 1 percent level. The R2 of the new equation is only
slightly lower than the R2 of Equation (38).
In order to test its ability to predict accurately, Equation (39) was
used to estimate the original visits data received from the U.S. Forest
Service. This is done in the following manner. Substituting the values
of W, F, and Si variables for Klamath Lake into Equation (39) gives:
V - 26,119.751 - 379.786 k (40)
where W, which is the sum of the swimming, boating, and water skiing use-
intensities listed in Table 1, is equal to 2; the fishing use-intensity
(F) is 1; and the lake size, in acres, is 98,560.
Substitution of the recreationists' average travel costs from each county,
which are listed in Table 3, gives an estimate of the number of visits to
Klamath Lake from each county. For example, using Klamath Lake and
Deschutes County, Equation (40) yields the following estimate:
V = 26,119.751 - 379.786 ($4.67)
V - 26,119.751 - 1773.601
V - 24,346.
Determination of the number of visits from each of the other counties in
the same manner, and summing over all of the counties, gives an estimate
of 243,211 visits to Klamath Lake. The same method is used to obtain
the estimates of total visits to the three other lakes in the study. The
number of visits estimated by Equation (39) for each lake are listed in
Table 4.
The total number of visits to the study area, that is, the sum of the num-
ber of visits to each lake, is accurately explained by the equation
(702,593 vs. 703,871). However, the distribution of the total visits among
the four lakes is not accurately predicted. The number of visits to Klam-
ath Lake and Lake of the Woods are over-estimated, while the number of
visits to Odell Lake are under-estimated. The estimate for Willow Lake is
quite accurate.
The particular manner in which the site characteristics are represented in
Equation (39) is believed to be responsible for the lack of predictive accu-
racy among individual lakes. Large variations exist in the values assigned
to the site characteristics in the equation. For example, lake size varied
53
-------
Table 4. A Comparison of the Forest Service Estimates of
Visits to Each Lake in 1968, and the Estimates
Derived from the Visits Equation
U.S. Forest Service Number of visits
estimates of number estimated by
Lake
Odell
Willow
TOTAL
of visits
146,491
266,327
180,304
109,471
702,593
V « f(W,F,Si,k)
243,211
335,331
14,968
110,361
703,871
from 320 acres to 98,560 acres; swimming, water skiing, and boating in-
tensity ranged from 1 to 9, and so forth. Since a direct and constant
relationship between visits and characteristics is Implied in Equation
(39), one would expect the magnitude of the site characteristics variables
to influence the estimated number of visits proportionately. As very high
values of the characteristics are observed, a very large estimated number
of visits will be obtained. If the values of the characteristics are gener-
ally low, a very low estimate of the number of visits will be forthcoming.
This phenomenon can be seen to exist in this study. To avoid this prob-
lem, the original U.S. Forest Service estimates are used to obtain the
aggregate demand functions and net economic value of each site. That is,
when q. is multiplied by V to obtain the aggregate demand model, Vq-, the
Forest Service's estimates of V for 1969 are used.
However, the estimated equation is used in another context. It is employed
to predict the number of visits subsequent to a change in water quality at
Klamath Lake by assigning new values to the site characteristics in the *
equation. Since the new values of the characteristics are larger than the
original values, and since the coefficients of these variables are positive
in the visits relationship, an increase in the number of visits is forth-
coming. However, the increase in the estimated visits should be expressed
as a percent change in total visits. Since Equation (39) predicts the .-".
total number of visits to all four lakes quite accurately, it is assumed
that it can adequately predict a percentage change in the total number of
visits. This allows us to estimate the number of visits to Klamath Lake »
after the water quality has been improved.
Estimation of Recreational Value
The equations estimated in the previous section are used to estimate the
demand for recreation at each of the four lakes in the study area. The
54
-------
recreationist's demand model for a lake consists of the k , p., and q.
equations and the values of the site characteristic variables of that lake.
An average individual's demand curve is illustrated in Figure 10. In the
figure, ^ is the critical daily on-site costs for the average person;
P! represents the average on-site costs per person per day; q. is the
length of stay per visit when daily on-site costs are at the critical
level, and ^ is the number of days the recreationist will stay, per visit,
if on-site costs were pT . It is here that the concept of consumer's sur-
plus is used. It is recalled that consumer's surplus is the difference
between the amount a consumer is willing to pay for a commodity and the
amount he actually has to pay for it. That is, consumer's surplus can be
measured as that portion of the area under the demand curve which lies
above the price of the commodity. This technique is straightforward when
the demand curve is shaped as the one illustrated in Figure 8. However,
the demand curve in Figure 10 has a unique property in that it does not
exist for quantities of recreation less than q... That is, the average
recreationist will either stay at the site a minimum of q. days per visit
or he will^not recreate at all. Therefore, it becomes a question of whether
the area ifL AB ~p~ or the area ABC is the appropriate measure of consumer's
surplus for a demand curve of this type. For the purpose of this study,
the area of the triangle, ABC, will be used to measure the net economic
value per visit. Work is continuing on the interpretation of the consumer's
surplus for the case of a truncated demand curve. This solution should be
viewed as one to facilitate the derivation of the remaining empirical esti-
mates. The area ABC can be determined mathematically:
value per visit. (40)
The total value of the site is determined by multiplying the value per visit
by the estimated number of visits to the site during the season.
The procedure described above is used to estimate the value of each of the
four lakes considered in this study.
Lake of the Woods
The use-intensities of the activities and the size of Lake of the Woods
were substituted into the k*, p*, and q^^ equations. The demand model for
Lake of the Woods is represented by the following equations:
k* - 23.617 + .0020 y 4- 10.435 PI (41)
p* - 2.458 4- .269 k - .004 k2 + .000000017 y2 (42)
.759 - .0064 k* 4- .0064 k 4- .0637 p* - .0637 p (43)
qx e 11
55
[f(Pl) dP;L] - [(px -
-------
*
pl I-
Figure 10. The Average Individual's Demand Curve, Per Visit,
for a Lake.
56
-------
Recreationists stayed at Lake of the Woods an average of 2 days, and spent
an average of $2.01 per day. Travel costs to Lake of the Woods averaged
about $15, while the average income of recreationists was just over
$10,500. Critical on-site cost was estimated to be $6.10, and critical
travel cost was about $66. The demand function estimated by incorporating
the above data into the demand model is:
qj . ..Ml - .0637 PI
This function is illustrated graphically in Figure 11. The value per
visit is:
6.10
f (e-821 " -°637 Pl) dp1 - [(4.09X1.54)] (45)
2.01
Value per visit $7.17 - $6.30 - $0.87.
The 1968 seasonal value of Lake of the Woods is obtained by multiplying
the per-visit value by the estimated number of Visits in 1968:
j
($0.87)(266,327) - $231,704.
The derived value of Lake of the Woods refers to the 1968 season. Any
inferences concerning estimated value for subsequent years requires addi-
tional assumptions. It must be assumed that the reactions of recreation-
ists remain constant, and the measured variables are not altered, or the
exact change can not be specified. Use of the lake in seasons other than
the summer season was not considered in this value estimate. For example,
ice fishing and duck hunting performed at Lake of the Woods during the
fall or winter are excluded. The above limitations also apply to the
value estimates of the remaining lakes.
Odell Lake
The following equations were estimated for Odell Lake:
k* = -18.076 + .0020 y + 10.435 pl (46)
p* - 1.641 + .269 k - .004 k2 + .000000017 y2 (47)
.759 - .0064 k* + .0064 k + .0637 p. - .0637 p, (48)
qi - e l J-
Recreationists stayed at Odell Lake an average of 2.4 days, spent $2.34
daily for on-site costs, and about $11 in travel costs. They had an aver-
age income of $9,063, and were estimated to have critical on-site costs,
p*, and critical travel costs, k*, of $5.57 and $24.71 respectively. The
incorporation of the above information into the demand model yields the
following demand function:
q « el-025 - .0637 PI (49)
57
-------
$6.10
$2.01
0.00
1.54 2.0
.821 - .0637P
K
Figure 11. The Average Recreationist's Demand Curve, Per
Visit, for Lake of the Woods.
58
-------
The value per.visit for 1968 is estimated as:
f (e1'025 * '°637 Pl) dPl - [(1.96)(3.23)] (50)
2.34
Value per visit - $7.17 - $6.33 - $0.84.
When this figure is multiplied by the number of visits for the 1968 season,
a total seasonal value of Odell Lake in 1968 is obtained:
($0.84)(180,304) = $151,455.
Willow Lake
Willow Lake is the smallest of the four lakes in this study. However, the
lake has approximately average value of the use-intensities for the vari-
ous activities. When these characteristics are substituted into the k ,
p.., and q_ equations, the demand model applicable to Willow Lake becomes:
k* -6.534 + .002 y + 10.435 Pj^ (51)
p* - 2.988 + .269 k - .004 k2 + .000000017 y2 (52)
= £.759 - .0064 k* + .0064 k + .0637 p* - .0637 PI (53)
The recreationists at Willow Lake recreated an average of 2.18 days per
visit, and spent $1.72 per day. They had an average income of $7,790,
and incurred approximately $6 in travel cost per visit. The estimated
critical travel cost averaged nearly $31, while the estimated critical
daily cost averaged $4.55. When p*, k*, and k are assigned average values
applicable to Willow Lake, the demand function for an individual visit is:
m e.888 - .0637 pi (54)
The average value per visit is:
4.55
r (e.888 - .0637 PI) d . [(2.83X1.82)] (55)
J *
1.72
Value per visit - $5.64 - $5.15 - $0.49.
The seasonal economic value for Willow Lake in 1968 is:
($0.49)(109,471) - $53,641.
59
-------
Klamath
The demand model for Klamath Lake, given its present characteristics and
use-intensity values , is :
k* = 9.132 4- .002 y + 10.435 p.,^ (56)
p* = 3.531 + .269 k - .004 k2 + .000000017 y2 (57)
= e.759 - .0064 k* + .0064 k + .0637 p^^ - .0637 PI ^5g)
The average stay per visit was 1.97 days, while average daily expenses at
the site were $1.84 per person. The average recreationist had an annual
income of $8,900, and allocated about $6.80 to travel costs per visit.
Average critical values of travel cost and on-site costs were estimated at
approximately $55 and $5.54 respectively. Using these values, the demand
function for Klamath Lake, as it now exists, is:
qi=e.801- .0637 PI
The economic value of Klamath Lake for the summer of 1968 is computed in
the same manner as for the other lakes:
mf w *f *
r (e.801 - .0637 p _ I(3.70)(1.57)]
»/ J.
1.84
Value per visit = $6.37 - $5.81 = $0.56.
The economic value of Klamath Lake, given its present characteristics, is
obtained by multiplying the value per visit by the number of visits to the
lake in 1968:
($0.56)(146,491) - $82,035.
60
-------
SECTION VII
THE THEORETICAL MODEL FOR ESTIMATING REGIONAL BENEFITS
The three preceding sections present methods for estimating the demand for
recreation and the economic value of four recreational sites. Before the
model is used to estimate the benefits resulting from water quality im-
provements at Klamath Lake, let us look at the procedures used to estimate
the local economic impact resulting from water quality improvements at the
lake.
As pointed out, the local community is often the recipient of indirect
benefits as the result of a project which increases the economic activity
of the region. To measure the magnitude of these benefits, it is necessary
to determine the economic structure of the region. Because of its unique
ability to portray the structure of an economy, a regional input-output
model was selected for use in this study.
An input-output model portrays the flow of goods and services throughout
the economy. It provides a means to measure the impact of changes in the
overall economic activity of the economy, resulting from a change in the
activity of any one segment of the economy. Two reasons have been cited
[Stoevener and Castle, 1965] why the interdependences portrayed by an
input-output model are important. They are: (1) the determination of the
aggregate level of regional secondary benefits, and (2) the distribution
of these benefits. Knowledge of the distribution of the regional benefits
among the various sectors of the economy may be especially important if
institutional arrangements for cost-sharing are to be made among the vari-
ous beneficiaries.
Input-Output Theory
Although some of the basic concepts had been developed earlier, Wassily
Leontief is usually credited with the introduction of input-output analy-
sis. In his first publication on the subject in 1936, Leontief introduced
input-output analysis as an empirical tool. Since Leontief's first publi-
cation, several extensions and alternative uses of the model have been de-
veloped. The input-output method has spread rapidly, and is a widely used
economic tool in the world today. The volume of literature relating to
input-output analyses is so large that several bibliographies have been
compiled (Riley and Allen [1955], Taskier [1961], and Input-Output Biblio-
graphy 1960-63 [1964]), and international conferences relating to input-
output analysis have been held.
An input-output model is illustrated by a "transaction matrix". It de-
scribes the flow of goods and services between the sectors of the economy
in a given time period. A sector is made up of a group of firms that carry
on similar types of business. The criteria used to define a sector will
61
-------
be discussed later in this section. A simplified transactions matrix is
presented in Table 5. The hypothetical economy is divided into three sec-
tors. Each of the sectors is listed twice in the matrix - once as a "pro-
ducing sector", indicated by the row heading, and again as a "purchasing
sector", shown by the column heading. The first three rows of the matrix
describe how the total output of Sector i (i - 1, 2, or 3) is distributed
among the various sectors of the economy. The first three columns describe
Sector j's (j « 1, 2, or 3) purchases of inputs from the various sectors
of the economy. Therefore, the x's, which represent the intersectoral
flows, represent the dollar value of goods and services sold by Sector i
to Sector j.
Table 5. A Hypothetical Transactions Matrix
CO
|4
s
o
0)
OT
I
o
3
0
M
fe
1
2
3
Value
added
Total
purchases
Purchasing Sectors
1
xll
X21
X31
Vl
Xl
2
X12
X22
X32
V2
X2
3
X13
X23
X33
V3
X3
Final
demand
Yi
*2
T3
V£
Total
output
Xl
X2
X3
The Final Demand column of the transactions matrix, represented by the
Y.'s (i 1, 2, 3) shows how much of the producing sector's output is con-
sumed as a "final good". Outputs allocated to final demand are not re-used
as intermediate inputs in producing other goods and services within the
economy under study. Final demand is referred to as the exogenous or
autonomous portion of the input-output system, because the level of demand
is not dependent upon the level of economic activity within the economy
being studied. The components usually assigned to final demand in an open
input-output model are consumption, investment and inventory accumulation,
purchases of the various levels of government, and exports.
The last column of the transaction matrix represents Total Output. Total
output of Sector i (X.) is the sum of its sales to other sectors and to
final demand:
62
-------
Xi = Xij + Yi (i = 1' 2' or 3)
The Value-Added row of the transactions matrix'is composed of the payments
made by the various sectors for "primary inputs" used in their production
processes. The components of the Value-Added row are payments to all
levels of government for services rendered, payments to households for
labor and entrepreneurial services, imports, depreciation of capital equip-
ment used in the production process, and depletion of inventories* A sec-
tor purchases produced inputs from the other sectors and produces a new
product of greater value. The increase in value is reflected in the pay-
ments made for the primary factors of production, which are recorded in
the Value-Added row.
At first it may appear that imports should not be included in the Value-
Added row, since they may consist of intermediate goods produced by other
economies. However, imports represent primary inputs into the economy
being studied, and they are being used in a production process within that
economy. Therefore, their value is reflected in the producing sector's
product, and must be included in the Value-Added row.
It should be noted that some of the components of final demand may also
purchase primary inputs. For example, wages paid to government employees
represent purchases of primary inputs. The symbol Vf in the transactions
matrix represents the value of all purchases of primary inputs made by
the components of the final demand sector. Although the V. portion of
the matrix adds additional information, it is not necessary to know these
values to solve the model.
The final row of the transactions matrix represents Total Purchases. Total
purchases of Sector j (X.) are the sum of all inputs used in the produc-
tion process of that sector:
3
X. = I x.. + V. (j - 1, 2, or 3) (62)
3 i=1 13 3
' t - . '
The model used in this study is referred to as an "open" model. However,
the model may be "closed" with respect to the household or government
component of final demand by including either or both, as an additional
sector in the processing portion of the ecqnomy. For example, the model
can be "closed" with respect to .households by removing consumption from
final demand, and payments to, households from value added, and forming,a
"Households" sector in the endogenqus portion of the model. Formation of
a households sector gives a more complete picture of the economy, because
it shows the relationship that exists between household income and expendi-
tures. However, the cost of obtaining the additional necessary informa-
tion prevented the construction of a household sector in this s£udy. The
model constructed in this study is, however, closed with respect to the,,,
local governments in the region. ;
63
-------
A final characteristic of the transaction matrix should be noted. The
total output of each sector is equal to its total purchases :
Xi = X. where (i - j)
This characteristic is a manifestation of Euler's Theorem, which states
that, under conditions of constant returns to scale (linear, homogenous
production functions), "total product is equal to the sum of the marginal
products of the various inputs, each multiplied by the quantity of its
input" [Stigler, 1966, p. 152],
Direct Coefficients Matrix
The transactions matrix is used to derive the direct coefficients matrix.
This step relies upon one of the basic assumptions of input-output analy-
sis. It is assumed that the level of inputs purchased by a sector is de-
pendent upon the level of total output of the purchasing sector. More-
over, inputs are purchased in a direct and constant relationship to the
output of the sector. From this assumption we can derive the direct co-
efficient, a . We recall from the transactions matrix that the x
represents Sector j's purchases -from Sector i, and that the total output
of Sector j was recorded in the Total Output column. It follows directly
from the assumption that:
XH
*ij ' xf (63)
where a.. » the direct coefficient, and
X. - total output of Sector j .
By solving Equation (63) for x.., and substituting it into Equation (61),
a new equation for total output is obtained:
3
X - I a X + Y (i - 1, 2, or 3) (64)
Direct coefficients indicate the value of inputs Sector j must purchase
from Sector i to produce one dollar of output. They illustrate the direct
interdependencies that exist between the sectors of the economy. For ex-
ample, an increase in the output of Sector 1 will lead to increased output
in Sectors 2 and 3 (providing a. . > 0) , because Sector 1 will require
additional inputs from Sectors 2 and 3 to produce its increased output.
The Direct and Indirect Coefficients Matrix
The direct coefficients do not, however, explain the full addition to
total output caused by an increase in demand of the Sector 1 product.
As Sectors 2 and 3 increase output tp satisfy the additional requirements
of Sector 1, they must also purchase more inputs from the various other
sectors to produce their increased 6utput. This causes another increase
64
-------
in the level of demand within the economy. Therefore, a change in the
output of one sector will cause direct and indirect increases in the out-
put of other sectors. The matrix of direct and indirect coefficients is
used to describe the total effect an exogenous change in the demand of one
sector will have upon the output of the entire economy.
The matrix of direct and indirect coefficients, or the "R" matrix, is de-
rived from Equation (64). Rearranging Equation (64) gives:
_ S±j X.j - Yr (65)
Rewriting Equation (65) in matrix notation yields:
X - AX'- Y, (66)
where X is the column vector of total output,
A is an nxn (where n = 3 in our example)
direct coefficients matrix, and
Y is the final demand column vector.
Factoring X out of the left side of the equation yields:
X(I - A) = Y (67)
where I is an identity matrix of the same
dimensions as the A matrix.
The identity matrix has the characteristic that, when multiplied by another
matrix of the same dimensions, it does not change the original matrix.
It serves the same purpose in matrix algebra that multiplying by unity
serves in arithmetic algebra. The main-diagonal cells of the identity
matrix contain unity, while all other cells in the matrix are zero.
Solving Equation (67) for X yields:
X * (I - A)"1 Y. (68)
The (I - A) or "R" matrix is also called the matrix of direct and indi-
rect coefficients. Each coefficient shows the output of Sector i needed
by Sector j to deliver one dollar of its output to final demand. It takes
into account the direct and indirect effects caused by a change in final
demand of one of the processing sectors. The availability of digital com-
puters has made the method of matrix inversion the most popular means of
obtaining the interdependence coefficients, since other methods using
simultaneous equations are more cumbersome.
Input-Output Assumptions
Three general assumptions are used in input-output analysis:
(1) Each commodity is supplied by a single sector.
65
-------
(2) The inputs purchased by each sector are dependent
upon the level of output of that sector.
(3) The total effect of carrying on several types of
production is equal to the sum of the separate
effects *. . -
The first assumption implies that each sector uses only one method of pro-
duction, and that only one primary output is produced by each sector. This
assumption requires satisfactory criteria by which to aggregate the numer-
ous economic activities in the economy into sectors. Ideally, two criteria
should be used in defining sectors. They are to aggregate industries with
similar input structures, and/or industries that produce strictly comple-
mentary outputs [Chenery and Clark, 1959]. It is seldom possible to
strictly follow these criteria when constructing a model, but they should
be adhered to as closely as possible, to insure more stable input coeffi-
cients.
Another point should be considered in the aggregation process. It should
be clear to the researcher how the model is to be used after its comple-
tion. More aggregation in some industries may be possible if they are
not expected to be important in the model's final use. Likewise, increased
specialization may be beneficial in the industries that are of major inter-
est in the analysis. For example, in this study it was felt that the
major portion of recreational spending would be spent on gasoline, grocer-
ies, prepared food, and lodging. Therefore, a sector was designed for
each of these categories, to obtain a more detailed analysis.
The second assumption, that the amount of inputs purchased by a sector
is a function of the level of the output of that sector, was mentioned
earlier. This is the most important assumption of input-output analysis.
However, it has drawn criticism from sources who feel it does not apply
in the real.world. These criticisms will be mentioned in the next sub-
section.
The third assumption of additivity disallows external economies and dis-
economies. It states that all the production processes carried on with-
in the economy are independent of each other. One production process
has no effect - either beneficial or detrimental - upon any other produc-
tion process.,
Limitations of the Model
Some doubt has been expressed concerning the ability of input-output
models to predict accurately. Many feel that the assumptions upon which
the model are based are too restrictive and unrealistic to give meaning-
ful predictions. Most of the criticisms have centered around the assumed
fixed direct coefficient because it ignores three changes that can occur
in an economy [Chenery and Clark, 1959]. They are: (1) changes in the
composition of demand, (2) changes in the relative prices of inputs, and
(3) changes in production technology. Of the three, a change in technol-
ogy is usually considered to have the greatest effect upon the direct
coefficients.
66
-------
Although the changes listed above will certainly affect the input coeffi-
cients in the long run, their effects may be minimal over shorter periods
of time. Even though new production processes become available, exist-
ing techniques are often used until capital items have depreciated and
new plants are built. In the same vein, changes in the composition of
demand and input substitutions usually occur gradually. Therefore, it
would seem that the assumption of fixed input coefficients would be justi-
fiable in the short run.
Cameron [1953], in a time series analysis of selected input coefficients
from the Australian model, concluded that his results generally supported
the assumption of fixed input coefficients in the short run. The most
important input coefficients appeared to remain relatively constant for
a period as long as a decade. The substitution that did occur between
inputs appeared to be caused by a change in the product-mix of the indus-
try, and not changing technology or price ratios. However, caution
should be exercised. One must be aware of the limitations of the model
and restrictions of the assumptions, to prevent misusing the model.
Regional Input-Output Models
Regional input-output models, such as the one constructed in this study,
have become a popular analytical tool. A wide variety of types of re-
gions have been analyzed. In most cases regions have been defined by
using political boundaries - that is, counties, states, or multi-state
regions. However, geographic characteristics, such as river basins,
have also been used to define the boundaries of study areas.
A regional model is constructed in the same manner as a national model.
Thus, the regional model is open to the same criticisms discussed earlier.
However, obtaining the data necessary to construct a regional transac-
tions matrix has been the dominant problem faced by the regional re-
searcher * Although it is expensive, extensive interviewing is often the
only available means to obtain the data required to construct a model.
Modifications of the Basic Model
The model constructed for this study is a regional input-output model,
but it differs slightly from the basic input-output model that was just
presented. The previous model was concerned with the technical input
structure of the various sectors. This gives the model a technical
orientation in that the input structure of each sector is determined by
the state of technology used by the sector. In the Klamath County model
the trade flows of the sectors of the economy are studied, instead of
the more technical input-output relationships. Therefore, the a±. *s
may more accurately be termed "trade" coefficients rather than technical
coefficients. A model of this type has been called a "from-to" model
[Leven, 1961].
There is one other conceptual difference between the Klamath County model
and the basic input-output model. In the latter model, all transactions
67
-------
involving capital items are removed from the endogenous flows. They are
then included in the investment component of final demand. This is neces-
sary, since investment purchases usually are not a function of the current
level of output.
However, in a from-to model, where the a 's are interpreted as trade
coefficients rather than input coefficients, it is not necessary to re-
move capital item purchases from the interindustry flows. Only the gross
flow of goods and services between the various sectors is relevant in the
from-to model.
The inclusion of investment purchases in the endogenous flows of the model
does, however, raise an important question: What effect does their in-
clusion have upon the stability of the trade coefficients? At first it
may appear that including investment purchases in the interindustry flows
would decrease the stability of the coefficients, since investment decis-
ions are not determined entirely by current output trends. That is, in-
vestment purchases are cyclical, and reflect conditions other than those
portrayed in the model. Therefore, the interindustry flows would vary
as investment purchases varied.
~ "i - *
To determine if the inclusion of investment purchases reduces the stability
of the coefficients, two types of investment cycles must be considered.
The first is the cyclical investment decisions of the individual firm. A
firm usually does not have a constant rate of investment over a given
period of time. Instead, a large investment is usually made during some
year, while smaller investments are made during other years. This type
of investment cycle may not significantly affect the stability of the
trade coefficients. One firm may purchase capital items during one year,
and another firm may invest the following year. Therefore, if the firms
are sampled in a random fashion, the observed level of investment may re-
flect a relatively stable yearly estimate for all of the firms in a sec-
tor.
The ot,her investment cycle of importance is that observed for the entire
economy. Aggregate investment varies from year to year^ This variation
is due to several factors, including the expectations of businessmen and
the availability of investment funds which may be subject to changes in
national fiscal and monetary policies. If data were gathered during a
year when investment spending was significantly above or below its usual
level, inclusion of investment purchases in the interindustry flows would
distort the coefficients. To determine if this had occurred in this
study, national aggregate investment figures were studied [Board of Gover-
nors of the Federal Reserve System, 1968]. The data indicated that in-
vestment spending at the national level increased sharply in the second
half of 1968. However, whether the Klamath County economy experienced
the same general increase in investment at that time cannot be determined.
Therefore, one can only conclude that the trade coefficients estimated
for the Klamath County model may have been subject to cyclical investment
fluctuations, but the extent of that effect, if any, could not be deter-
mined.
68
-------
SECTION VIII
CONSTRUCTION OF THE FROM-TO MODEL AND
AN ANALYSIS OF THE LOCAL ECONOMY
The first step in the construction of the from-to model is to define the
study area. Klamath County was selected as the study area, primarily
because it includes the communities that would benefit from expanded use
of Klamath Lake. Defining the county as the study area also offers addi-
tional benefits. Secondary data that would aid in the study are avail-
able on a county basis. Also, defining the study area to coincide with
political boundaries is advantageous, since the model may provide useful
information to county planning and development groups. A map of Klamath
County is provided in Figure 12.
Sampling Procedures
Since sampling techniques were to be used to obtain the data required to
construct the model, a listing of all the business firms in Klamath County
was obtained. Three secondary sources were relied upon to compile the
population. They are: (1) the 1968 telephone directory of Klamath Falls
and surrounding communities, (2) a listing of business firms in Klamath
County, received from the Klamath County United Good Neighbors, and (3)
the 1967 Klamath Falls City Directory. A final population included
1,840 business firms.
Each firm in the population was then placed in the appropriate sector of
the model. Table 6 contains the sectors of the model and examples of
the types of firms in each sector. The Household sector is also defined
in the table, although it is not included as a sector in the processing
portion of the matrix. A firm with multiple economic activities, such
as selling and servicing, was placed in the sector that described its
largest income-producing activity.
After each firm had been assigned to the appropriate sector of the model,
most of the sectors in the model were stratified so that the firms in
each sector could be grouped into more homogenous categories than a sec-
toral grouping alone could provide. By increasing the homogeneity of a
group of businesses, a smaller sample could be used to obtain informa-
tion about the businesses in each stratum.
Two types of stratification were used. All sectors except Agriculture,
Professional Services, Service-Oriented, Resorts and Marinas, and Local
Government were stratified according to size. That is, each firm in the
sector was placed into a size group, usually large, medium, or small,
within the sector. For example, if the gross sales of a firm were thought
to be large, relative to the other firms in the sector, the firm was
placed in the large-firm stratum.
69
-------
Odell
Lake
Crater Lake
National Park
Klamath /" Highway 140
alb
Figure 12. Klamath County, Oregon.
70
-------
Table 6. Description of the Sectors in the Klamath
County Model
Sector
number Sector title
Sector description
1, Agriculture
2. Agricultural Services
3. Lumber
4. Manufacturing and
Processing
5. Lodging
6. Cafes and Taverns
7. Service Stations
8. Construction
9, Professional Services
1Q. Product-Oriented
1 (wholesale and retail)
11. Service-Oriented
Farms, ranches, and feedlots.
Farm implement dealers, farm coopera-
tives, feed, seed, and fertilizer stores,
livestock auction yards, and irrigation
pump dealers.
Logging, log hauling, lumber and ply-
wood mills.
Potato processors, creameries, bottling
companies, meat and poultry processors>
machine manufacturing, trailer manu-
facturers, and stone, clay, and glass
manufacturers.
Hotels, motels, trailer parks, and
apartments. »
{-,
Businesses that sell beverages and pre-
pared food that may be consumed on the
premises.
Gasoline bulk plant distributors, ser-
vice stations, and heating fuel dis-
tributors.
General building contractors, electriea^
and plumbing contractors, sand and gravel
operations, asphalt paving contractors,
carpenters, concrete manufacturers, exca-
vators, land levelers, road and highway
contractors, roofing and painting contrac-
tors, masonries, and well-drillers.
Doctors, dentists, lawyers, accountants,
architects, surveyors, engineers, hos^
pitals, veterinarians, ambulance ser-
vices , and nursing homes.
All firms that receive the largest part
of their income from the sale of pro-
ducts at the wholesale or retail level
that are not included in other sectors.
Examples: utility companies, department
stores, specialty stores, drug stores,
and bottled beverage distributors. j
Firms that receive the largest part of
their income from the sale of services.
(Continued on following page)
71
-------
Table 6. (Continued)
Sector
number Sector title
Sector description
12. Communications and
Transportation
13. Financial
14. Grocery
15. Resorts and Marinas
16. Automotive
17. Local Governments
Households
Examples: beauty and barber shops,
insurance and real estate agencies,
repair stores, laundries, churches,
social organizations, and labor unions.
Trucking firms, railroads, airlines,
buses, radio, television, telephone,
telegraph, newspapers, and television
cable.
Banks, savings and loan associations,
loan companies, and securities invest-
ment businesses.
Firms which sell food for pff-premise
consumption. Examples: grocery;,
stores, seafood stands, meat stores,
and fruit stands.
Stores at recreational sites, marinas,
and boat dealers.
Auto and trailer sales, tires, parts
and accessory stores, and auto repair
shops.
County and city governments, school
districts, and special taxing districts.
All private individuals.
The Professional Services, Service-Oriented, and Resorts and Marinas
sectors were stratified on the basis of the economic activities within
the sector. For example, in the Professional Services sector, physi-
cians were put in one stratum, dentists in another stratum, accountants
in a third, and so forth. Alternatively, each of these strata could
have been considered as an additional sector. This would have led to
a much larger number of sectors than were used in the study. However,
it was felt that the benefits from increased homogeneity in the smaller
sectors were not sufficient to compensate for the increased difficulty
of collecting data for a more highly disaggregated model.
Data for the Agriculture and Local Government sectors were not collected
by the same procedure. They will be discussed later in this section.
72
-------
Determination of the Sample Size
To estimate the sample size, the variances of the variables to be esti-
mated must be known. Since estimates of the variances were not avail-
able, other techniques had to be used to determine the sample size. Two
factors were considered. The first was the amount of funds available
for collecting the data; the other was the sampling rate used in pre-
vious input-output studies in Oregon. In previous studies by Bromley
[1967] and Stoevener [1964], the sampling rates were between 25 and 30
percent of the total population.
After considering these factors, a sample size of 500 was selected. This
is equal to about 27 percent of the population. A 10 percent oversample
was drawn, to allow for incomplete questionnaires and refusals. There-
fore, the total sample consisted of 550 firms.
Allocation of the Sample
Three criteria were considered to allocate the total sample among the
various sectors. They are: (1) the number of firms in each sector, (2)
an estimate of the gross sales of each sector, and (3) the amount of
variability in size and types of economic activity in each sector. In
the case of the first criterion, an allocation of the sample was made,
based entirely upon the number of firms in each sector. If a sector
contained 10 percent of the businesses in the county, 10 percent of the
sample was allocated to that sector.
The second criterion was used to give a weighting factor to each sector,
based upon its total output relative to the total output of the entire
economy. In order to do this, it was necessary to obtain an estimate
of the total output of each sector. Secondary sources were used to ob-
tain these estimates. Even though complete sales data were not avail-
able for all the sectors, it was possible to get a general indication of
the volume of sales. These estimates were then used to allocate the
sample on the basis of the total output of each sector.
As mentioned previously, data were not available to estimate the vari-
ances of the parameters to be estimated. However, a subjective measure
of variability was considered in the allocation of the sample. Two types
of variability were studied. The first was the variation in the size
of firms in each sector. The other dealt with the amount of diversifi-
cation as to the types of economic activity in the sector.
The two sample allocations, based on the number of firms in the sector
and the total sales of the sector, provided a range for the sample size
for each sector. The variability within each sector was then considered.
If the variability was considered to be large, the actual Cample size
allocated to the sector was taken from the upper portion of the range
that had been determined. Table 7 lists the sectors and the allocation
of the sample.
73
-------
Table 7. Distribution of the Sample Among
the Sectors of the Model
Number of Firms
Sector Population Sample
1. Agriculture * *
2. Agric. Services 25 17
3. Lumber 39 17
4. Manufacturing & Processing 36 20
5. Lodging 165 36
6. Cafes & Taverns 119 26
7. Service Stations 135 34
8. Construction 156 40
9. Professional Services 160 33
10. Product-Oriented 259 100
11. Service-Oriented 442 123
12. Communications & Transportation. 60 23
13. Financial 30 15
14. Grocery 95 29
15. Resorts & Marinas 15 4
16. Automotive 104 34
17. Local Governments * *
TOTAL ECONOMY 1,840 551
: _ _
Secondary data was utilized in these sectors.
Once the sample size had been determined for each sector, it was neces-
sary to allocate the sector sample size among the various strata in each
sector. All of the firms classified as "large" were included in the
sample. A random sample was then drawn from each remaining strata of
each of the 15 sectors that were sampled. The sample drawn included 551
firms.
Local Governments
Since data concerning local governments were readily available, it was
not necessary to include the various units of government in the county
74
-------
in the interviewing process. The expenditures of all governmental units
were obtained for the 1967-68 fiscal year. These expenditures were then
allocated to the various sectors in the model, with the assistance of the
bookkeeper or purchasing department of each unit of government. These
data were used to fill in the Local Governments column in the transactions
matrix.
Agriculture
Agriculture, being the second largest industry in Klamath County, is an
important sector in the model. The 1964 Census of Agriculture estimated
that there were more than 1,000 farms in Klamath County. However, more
secondary data were available for agriculture than for any other sector.
It was felt that the necessary estimates could be determined from the
available data, without the collection of primary data.
Sampling Results
Personal interviews were conducted with each firm in the sample. It be-
came obvious in the early stages of data collection that 500 responses
would not be obtained from the 551 firms in the sample. Therefore it was
necessary to draw replacements for 175 non-responding firms. The alloca-
tion of,the second sample was determined by the number of firms in each
stratum that did not respond in the first sample. If four firms did not
respond in a particular stratum, four additional firms were drawn from
that stratum to replace the non-responding firms. Completed question-
naires were eventually obtained from 438 firms.
Several factors contributed to the low response rate. First, relying upon
secondary sources to compile the list of businesses resulted in including
firms in the sampling frame that were no longer in business. Lists of
businesses become obsolete very rapidly, due to the rate of business turn-
overs .
A second factor contributing to the non-response rate was the type of data
being collected. In order to construct the model, detailed financial
data were required from each firm in the sample. Most of the refusals
resulted from firms who considered the data to be confidential and, there-
fore, would not release it.
The type of businesses in the study area also contributed to the poor re-
sponse. Many of the businesses in the county are sub-divisions of larger
companies. In many cases they did not have the detailed information
available at their Klamath County office. The head offices of these
companies were contacted by mail and telephone. However, the interview-
ing procedures used in the study were not well designed for these non-
personal contacts, and many firms did not reply to the requests for in-
formation. Other firms indicated they did not maintain the type of data
requested for individual branch offices of the company, and therefore
could not respond. Furthermore, it was not possible to determine the
owners of some businesses such as self-service laundromats and car washes.
75
-------
Therefore, some firms of this type could not be contacted. The 438 com-
pleted interviews represent nearly 24 percent of the firms in the county.
The questionnaire used to obtain the data is included in Appendix B.
The Klamath County Economy
Transactions Matrix
The transactions matrix, presented in Table 8, was constructed from the
collected data. As mentioned earlier, each sector of the economy is
listed at the left, and the numbers at the top of the matrix correspond
to the numbered sectors at the left. Those listed at the left represent
the selling sectors, while those across the top indicate the purchasing
sectors. The figures in the cells of the matrix indicate the value of
goods and services sold by the sector at the left to the sector at the,
top. For example, reading across the Agriculture row shows that it sold
$6,189,800 worth of goods and services to Agriculture (intraindustry
sales), $602,220 to Agricultural Services, zero to Lumber, $9,484,110
to Manufacturing and Processing, and so on across the row. The distribu-
tion of sales of each of the other 17 sectors can be determined in the
same manner.
The purchases of each sector of the economy can also be determined from
the transactions matrix. This is done by reading down the column of a
sector. For example, reading down the first column shows that Agricul-
ture purchased $6,189,600 of goods and services from itself, $4,445,044
from Agricultural Services, $75,660 from Lumber, $168,712 from Manufac-
turing and Processing, and so on down the column.
The first 17 rows and columns comprise the endogenous portion of the
transactions matrix. Row 18 is the sum of the first 17 rows in each
column. The figures indicate the total value of goods and services the
sector purchased within the local economy. The figures provide a general
indication of how much that sector depends upon the local economy. The
larger the figure, relative to the total purchases of the sector (Row 23),
the greater the magnitude of dependence of that sector, in terms of its
inputs, upon the other sectors of the local economy.
Rows 19-22 comprise the value-added portion of the matrix. The House-
hold row (19) indicates the value of services purchased from private
individuals. It includes such payments as wages, returns to entrepre-
neurial services, interest, dividends, and rent. This figure indicates
another characteristic of the various sectors - the larger the payments
to Households, relative to the total purchases of the sector, the more
labor-intensive is the industry.
The Import row (20) depicts the purchases of goods and services from out-
side the Klamath County economy. This provides a measure of the degree
of self-sufficiency of the economy. The large volume of imports purchased
by the sectors in this model indicates that the economy of Klamath Countv
is not nearly self-sufficient.
76
-------
Tabu 8. Transactions Matrix showing Interindustry Flova in Dalian,
Klamath County, 1968 (Rounded to Nearest $1,000)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17
18.
19
20.
21.
22.
23.
Agriculture. * . . * .
Agric. Service*..
Manufacturing 6
Processing
Cafes & Taverns*.
Service Stations.
Construction
Professional
Services * * f , .
Product-Oriented .
Service-Oriented .
Communications &
Transportation .
Resorts &
Local Gov* t ...
Summation^-1'
Depreciation &
Negative Inven-
tory Changes...
Total Inputs5'...
1
6190
4445
76
169
0
0
931
175
132
918
430
244
665
26
5
218
1363
15985
9629
61
573
2607
28854
2
602
204
o
*
o
1
83
0
15
371
57
760
128
o
o
77
40
2338
1167
7203
130
289
11129
3
o
37
9079
149
*
19
660
260
39
1960
169
12880
620
48
o
1000
1204
28122
22774
15634
8166
5123
79819
4
9484
203
143
A
o
*
149
228
626
46
2584
146
o
o
68
96
13799
3582
4539
645
591
23155
5
Q
3
0
82
o
0
47
33
17
773
162
331
96
o
o
o
96
1636
1590
502
137
461
4326
6
35
3
Q
720
o
0
561
104
7
1871
203
54
17
174
0
o
41
3285
2213
344
327
294
6464
7
o
0
0
o
0
1685
64
1 C
346
100
146
49
o
o
326
51
2765
2493
10283
569
284
16394
P U ]
8
Q
12
425
294
g
18
437
2214
37
971
292
322
148
o
o
193
70
5439
4760
7383
504
527
18613
1 C H A
9
3
Q
26
*
0
52
28
261
134
230
59
0
0
58
79
951
8147
4108
758
776
14740
SING
10
0
375
375
Q
0
213
927
1ft
993
257
1887
82
g
o
445
986
6765
8496
27114
4325
863
47564
SEC
11
46
3
21
*
0
95
231
815
849
424
48
0
0
128
297
3035
6103
5937
917
488
16480
TOR
12
12
Q
1
o
0
362
7
1Q
242
15
100
17
19
0
92
810
1697
8660
13514
3707
2475
30053
13
0
0
7
*
1
44
173
305
109
65
o
0
5
42
762
1526
3354
291
147
6079
14
160
0
g
3887
Q
0
35
22
1743
110
429
17
1009
0
7
57
7466
2395
13419
482
269
24060
15
Q
6
Q
26
Q
0
92
2
2
64
23
0
17
0
12
12
29
274
109
281
22
17
703
16
Q
3
0
ft
0
41
23
20
224
254
182
433
o
o
1064
60
2324
3338
13267
378
629
19936
17
j
82
Q
314
*
1
161
565
11 5
782
314
103
0
43
1
343
75
2899
8466
907
958
0
13230
19
88
1574
164
1886
4145
6389
10505
6232
12554
25394
11768
4833
3325
21822
684
14700
1892
127953
127953
20
12223
4108
66842
11621
117
7
644
629
411
5895
668
2577
148
651
3
379
0
106924
106924
21
58
703
1589
3363
50
7
108
6818
1158
2106
253
1844
0
176
1
458
5942
24002
24002
22
0
316
912
222
0
21
37
28
53
1037
72
13
0
84
9
344
0
3147
3147
23
28854
11129
79819
23155
4326
6464
16394
18613
14740
47564
16480
30053
6079
24060
703
19936
13230
361597
95449
127849
22889
15840
623623
Hay not SUB, due to rounding error.
Number in cell rounds to zero.
-------
Columns 19 through 22 comprise the final demand for goods and services
sold by the sectors listed at the left of the matrix. The four compo-
nents of final demand indicate the major uses of the goods and services
sold. The Household column (19) represents the value of goods and ser-
vices sold to individuals, while the Government column (21) shows the
value of sales to state and federal governments. Column 20 represents
exports from Klamath County by the various sectors, while Column 22
indicates positive inventory changes. Column 23 summarizes total sales
by each sector. The remaining rows and columns of the transactions ma-
trix are self-explanatory.
Direct Coefficients Matrix
The direct coefficients, or "A" matrix, is presented in Table 9. The
matrix is utilized by reading down the columns in order to determine the
input structure of the sectors of the economy. In most cases, the a 's,
which represent Sector j's purchases per unit of output, reveal more
about the structure of a sector than the absolute magnitude of inter-
industry sales depicted in the transactions matrix.
The first column of the "A" matrix shows that Agriculture must purchase
21 cents worth of goods and services from itself if it is to increase
its output by one dollar. Continuing down the column, Agriculture must
also purchase 15 cents worth of goods and services from Agricultural Ser-
vices; less than one cent from Manufacturing and Processing, and Lumber;
zero from Lodging, and Cafes and Taverns; and so on down the column.
The Summation row (18) shows that Agriculture purchases over 55 cents
worth of goods and services from the local economy for every dollar of
output. Row 19 shows that Household incomes increase 33 cents per dollar
increase in sales of the Agriculture sector.
Characteristics of the Economy
Some of the characteristics of the local economy can be studied, using
the numbers in the transactions and direct coefficients matrices. A
breakdown of the sales of each of the 17 sectors is given in Table 10.
The dollar value and percentages of sales are separated between the local
economy and final demand. It is interesting to note that only the Agri-
culture and Communications and Transportation sectors sell more than one-
half of their total output to the businesses in the local economy (57 and
69 percent, respectively). Most of Agriculture's local sales (95 percent)
are to itself and Manufacturing and Processing; the Lumber sector pur-
chases almost 62 percent of Communications and Transportation interindus-
try sales. This is primarily due to the use of transportation facilities
for shipping lumber and wood products out of the county.
Five sectors sell less than 10 percent of their total output to the sec-
tors of the local economy (see Table 10). They are: Lodging (0.33 per-
cent), Cafes and Taverns (0.60 percent), Professional Services (3.83 per-
cent), Grocery (5.52 percent), and Resorts and Marinas (0.93 percent).
78
-------
Table 9. Direct Coefficients Matrix, Klamath County, 1968
VO
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14,
15.
16
17.
18.
19
20.
21
22.
Agric. Services.. .
^"fflbflr. .!...... >
Manufacturing &
LodfeinK ........
Cafes & Taverns . . .
Service Stations..
Professional
Services ........
Product-Oriented. .
Service-Oriented. .
Communications &
Transportation. .
Resorts &
Summation
Depreciation &
Negative Inven-
tory Changes ....
I
2145235
.15*0545
.0026222
.0058472
0
0
.0322691
.0060485
.0045879
.0318111
.0149091
.0084421
.0230436
0009011
.0001560
0075415
,0472506
.5540078
.3337123
.0020977
0198452
.0903370
2
0541127
.0182977
o
.0000182
o
.0000496
.0074740
o
0013681
.0333225
.0051041
.0682645
.0115460
o
0
0069620
. 0036119
.2101313
. 1048810
.6472559
0117208
.0260110
3
o
.0004619
1137430
.0018617
0000018
.0002331
.0082637
0032604
0004858
.0245554
.0021204
.1613647
.0077651
.0006067
o
.0125246
,0150783
. 3523266
.2853242
. 1958690
.1023003
.0641799
4
4095844
.0087807
0061852
.0000057
Q
.0000158
.0064210
0098342
0010641
.0270465
.0020055
.1115995
.0063175
o
o
.0029208
. 0041350
.5959160
.1546968
. 1960159
.0278680
.0255033
5
o
.0007046
o
.0188407
o
0
.0108871
0075774
0028599
.1787581
.0374578
.0766000
.0222967
0
o
0
.0222105
. 3781929
.3675640
. 1159689
.0316050
.1066693
6
0054769
.0004716
o
.1113510
0
0
.0086890
0160701
0010932
,2894551
.0313445
.0084104
.0025868
0269123
0
o
.0063460
.5082068
. 3423530
.0532527
.0506385
.-0455490
P U R C H
7
o
0
0001830
o
o
0
.1028092
.0026576
.0009287
.0211160
.0060842
.0089191
.0029653
o
o
.0198870
.0030832
.1686333
.1520755
.6272337
.0347320
.0173256
A S I N G
8
0
.0006706
0228384
0157952
0003481
.0009698
.0234820
1189359
0019959
.0521561
.0156754
.0172840
.0079256
o
o
.0103490
.0037769
.2922030
.2557389
.3966703
.0270772
.0283106
SECT
9
0008005
.0002068
o
0017970
0000293
0
.0035185
0019020
0005697
.0176928
.0090787
.0156299
.0040125
0
0
0039508
,0053372
.0645257
.5527168
.2786876
.0514301
.0526398
0 R
10
o
0
0120870
.0078912
o
0
.0044844
0194974
0003736
.0208713
.0053941
.0396769
.0017154
0001717
0
0093467
,0207205
.1422302
.1786292
.5700667
.0909371
.0181367
11
o
.0027971
0001820
.0012742
000010n
0
.0057526
.0140374
.0046699
.0494391
.0515277
.0257284
.0029308
0
0
.0077758
.0180357
.1841608
.3703383
. 3602376
.0556542
.0296090
12
o
.0004057
o
.0000479
o
0
.0120488
.0002456
.0006469
.0080421
.0005024
.0033210
.0005513
. 0006252
o
.0030664
.0269524
.0564557
.2881784
.4496803
.1233446
.0823409
13
o
0
o
0
0010795
.0000604
.0002445
.0072518
.0017290
.0285294
.0501277
.0178865
.0106717
0
0
.0007480
.0069547
.1252831
.2509756
.5517197
.0478354
.0241862
14
0066699
0
.0003325
.1615655
0
0
.0014430
.0009029
.0004641
.0724594
.0045806
.0178337
.0006948
.0419426
0
.0002876
.0023593
.3115359
.0995215
.5577133
.0200398
.0111896
15
o
.0086761
0
.0374943
0
0
.1311882
.0021342
.0025126
.0907160
.0327138
0
.0237859
0
.0021342
.0173536
.0417669
.3904757
.1550822
. 3992442
.0312953
.0239026
16
o
. 0001529
o
0
.0000072
0
.0020521
.0011785
. 0009 786
.0112363
.0127375
.0091382
.0217047
o
o
.0543582
.0030266
.1165707
.1674407
.6654813
.0189422
.0315651
17
.0000548
.0061895
0
.0237040
.0000363
.0000654
.0121899
.0426874
.0087201
.0590806
.0237012
.0077579
o
0032325
. 0000401
0259638
00566 76
2190911
.6399147
.0685791
0724151
0
May not sum, due to rounding error.
-------
Table 10. Distribution of Sales of Each Sector in the Klamath County Economy
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
Sector
Manufacturing & Processing...
Lodging
Product-Oriented * ...
Communications & Trans-
Financial
Interindus t ry
sales
$16,484,515
5,050,809
10,311,758
6,064,412
14,407
38,804
5,100,946
4,906,159
563,723
13,132,289
3,718,892
20,785,067
2,605,379
1,327,255
6,530
8,054,992
5,395,930
Sales to
final demand
$12,369,200
6,068,819
69,507,488
17,091,036
4,311,338
6,424,758
11,292,742
13,707,191
14,176,275
34,431,310
12,761,510
9,267,485
3,473,132
22,733,102
696,323
15,880,679
7,833,912
Percent of
sales sold to
local economy
57.13
45.47
12.92
26.19
0.33
0.60
31.12
26.36
3.83
27.61
22.57
69.16
42.86
5.52
0.93
40.40
40.79
Percent of
sales sold to
final demand
42.87
54.53
87.08
73.81
99.67
99.40
68.88
73.64
96.17
72.39
77.43
30.86
57.14
94.48
99.07
59.60
59.21
o
CO
-------
The reason for the low percentages is that each of these sectors primar-
ily serves the needs of the Household sector, which is exogenous in this
model.
As mentioned earlier, Row 18 of the direct coefficients matrix (Table 9)
indicates the value of each sector's purchases, per dollar of sales,
that are obtained from the local economy. Only three sectors purchase
more than one-half of their goods and services from the local economy.
They are: Agriculture (55.4 percent); Manufacturing and Processing
(59.6 percent); and Cafes and Taverns (50.8 percent). The Communica-
tions and Transportation sector is least dependent upon the local econo-
my, as it purchases only 5.6 cents worth of goods and services, per dol-
lar of output, from local businesses.
In absolute terms (Table 8) , Lumber purchases more goods and services
($28,122,000) from the Klamath County economy than any of the other sec-
tors. Agriculture ranks second ($15,985,000), followed by Manufacturing
and Processing ($13,799,000). This gives some indication of the impor-
tance of these sectors in the economy.
The Household coefficients (a^'s) in Row 19 of the direct coefficients
matrix are important because they indicate the amount household incomes
will rise if the output of Sector j increases one dollar. They repre-
sent the direct effect a one-dollar change in output will have upon
household incomes. It is interesting to note that the Local Government
sector has the largest a, . (.64) in the economy. This indicates that
payrolls and other payments to households account for a large portion of
the budgets of the various units of local government. The Professional
Services and Service-Oriented sectors rank second and third, with a^.'s
of .55 and .37 respectively. One would expect the service sectors to
have larger household coefficients, since they are labor-intensive in-
dustries. Grocery and Agricultural Services have the smallest household
coefficients, .0995 and .1049 respectively.
As noticed earlier, the large quantity of imports (Row 20 of Tables 8
and 9) purchased by the various sectors in the model indicates that the
economy is highly dependent upon the "rest of the world" as a source of
goods and services. The large importers are those sectors that deal in
products that cannot be produced within the economy. They include Agri-
cultural Services (64 percent of purchases are imports), Product-Oriented
(57 percent), Service Stations (62 percent), Grocery (56 percent), and
Automotive (67 percent). Agriculture imports less, in absolute and rela-
tive terms, than any other sector.
A final characteristic of the Klamath County economy can be seen by
studying the Export column (20) in Table 8. The fact that all of the
sectors (except Local Government) export some goods and services illus-
trates that the economy serves as a trading center for other communities
outside the county. This is especially true at the wholesale trade level.
The largest exporters are the basic industries of the economy. Agricul-
ture exports more than $12 million, Lumber $66.8 million, and Manufacturing
81
-------
and Processing about $11.6 million. A large portion of the exports of
the latter sector are agricultural commodities that have been processed
by local firms.
The foregoing discussion illustrates that, like most small regional econo-
mies, the Klamath County economy is highly specialized. Lumber and Agri-
culture are the basic industries of the economy. Many of the goods and
services used in the economy must be imported, while the primary indus-
tries export large quantities of products.
82
-------
SECTION IX
APPLICATION OF THE INPUT-OUTPUT MODEL
The Direct and Indirect Coefficients Matrix
The Xl-A) or direct and indirect coefficients matrix is presented in
Table 11. It contains 17 rows and 17 columns, one for each of the 17
sectors of the economy. Because of the direct and indirect effects ex-
plained in Section VII, the coefficients in the (I-A)"1 matrix are larger
than those in the corresponding cells of the direct coefficients matrix.
That is, the coefficients in the (I-A) matrix indicate the total in-
crease in output of a sector resulting from a change in demand for the
output of a sector. For example, assume that there is a one-dollar in-
crease in final demand for the products of Agriculture. This sets into
motion a series of changes in the output of all the sectors of the econ-
omy. When the change has worked itself out, Agriculture's output will
have increased $1.29; Agricultural Services, 20 cents; Lumber, one-half
cent; and Manufacturing and Processing one cent, and so on (reading down
the Agriculture column) .
Output Multiplier
The eighteenth row of the (I-A) matrix is the sum of the first 17 rows
of each column. The figures in the row represent the change in total
output of the economy resulting from a one-dollar change in final demand
of the sector listed at the top of the column. For example, a one-dollar
increase in final demand of Agriculture will cause the output of the en-
tire economy to increase $1.82. This is called the output multiplier of
the sector. The magnitude of the output multiplier of each sector depends
upon the quantity of goods and services the sector purchases from the
local economy. Earlier it was pointed out that Communications and Trans-
portation purchased only 5.6 percent of its purchases from the local econ-
omy. The output multiplier of that sector is small (1.07), as would be
expected. Conversely, Manufacturing and Processing purchases more of its
goods and services from the l^cal economy than other sectors , and the out-
put multiplier of the sector is the largest (1.96) in the economy. The
output multiplier for each sector is listed in Column 2 of Table 12.
Income-Output Coefficients
Another useful tool is the "income-output" coefficient (1^) listed in
Column 3 of Table 12. These coefficients are computed as follows:
a r
ik
83
-------
Table 11. Direct and Indirect Coefficients Matrix, Klamath County, 1968
1
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13
14.
15.
16
17.
18.
Agric. Services....
Manufacturing &
Cafes & Taverns ....
Service Stations...
Professional
Product-Oriented. . .
Service-Oriented. . .
Communications &
Transportation. . .
Financial
Resorts &
Marinas
Summation^-
1
1.2924189
.2034219
.0050732
0101022
.0000440
.0000316
.0505540
0143484
.0071093
.0561251
.0260502
.0319157
0334278
.0014715
.0002046
0158705
.0653672
1.8155362
2
0715281
1.0299960
0008269
0010847
0000166
.0000550
.0126468
0022169
0019811
.0400509
.0082094
.0738215
0141072
0001595
. 0000116
0094640
0103294
1.2765056
3
0017655
.0010798
1 1289852
00321Q4
0000156
.0002715
.0137084
0063512
0009765
.0329186
.0043800
.1854346
0095785
0009295
.0000012
0169545
0232081
1.4297781
4
5303589
.0925499
0098114
0000303
.0000441
.0302422
0183536
0042238
.0547837
.0140249
.1288916
0206359
0007187
.0000843
0110564
0351263
1.9557740
5
0114250
.0030697
0031961
1 0000328
.0000198
.0160474
0155995
0036325
.1904989
.0433469
.0899685
0237899
0002092
.0000030
0041341
0305327
1.4569958
P U R C H
6
0705473
.0128891
0060240
0000180
1.0000333
.0166331
0286043
0021509
. 3094692
.0378958
.0391008
0063267
0283062
.0000118
0058081
0188689
1.7024360
A S I N G
7
0002174
.0001018
0006957
0000063
.0000049
1.1151830
0043592
0011723
.0255200
.0080439
.0117901
0039979
0000286
. 0000002
0240042
0046023
1 2001299
S E C T 0
8
0100951
.0026726
0303902
0004081
.0011121
.0316320
1 1378045
0026343
.0657223
.0207097
.0309500
0103770
0001196
0000019
0148427
0081818
1.3866376
R
9
0022119
.0006590
0003767
0000355
.0000039
.0046137
0031860
1 0007314
.0197731
.0102899
.0173916
0043564
0000397
0000006
0048693
0066366
1.0773725
10
0048521
.0010560
0146981
0000123
.0000288
.0071525
0242193
0007632
1.0259884
.0073289
.0453898
0026005
0003072
0000017
0116814
0234121
1 1786482
11
0016276
.0034530
0015116
0000224
.0000209
.0084350
0192585
0052421
.0567059
1.0560206
.0311355
0037810
0001061
0000011
0104146
0214906
1 2218764
12
.0006905
0002068
0000026
.0000038
.0140276
0009295
.0106190
.0015324
1.0044428
0007713
0007512
0000012
0044683
0275880
1 0694795
13
0004275
.0003060
0007493
0007721
0010962
.0000720
.0015410
0104380
0021429
.0338895
.0541728
.0215342
0000550
0000004
0020837
0094686
1 1499592
14
0988687
.0171587
0032411
1703329
0000079
.0000115
.0080539
0063725
0013759
.0880268
.0083282
.0444174
0047084
1 0439570
0000159
0034427
0112854
1 5096049
15
0217108
.0130502
0020454
0398947
0000340
.0000152
.1496507
0089977
0035552
.1049830
.0397294
.0137089
0264103
0002099
1 0021440
0248025
0474299
1.4983721
16
0001674
.0002722
0002621
0002817
0000340
.0000041
.0028894
0024012
0012092
.0142181.
.0157132
.0113082
0233338
0000249
.0000002
1 0580259
004 3110
1.1344570
17
0142783
.0089656
0024848
0259868
.0000574
.0001174
.0167171
0513798
.0092312
.0679513
.0275269
.0168817
0019919
0034470
.0000428
0299144
1.0093432
1.2863176
CO
May not sum, due to rounding error.
-------
Table 12. Output and Income Multipliers and Income-Output
Coefficients for Each Sector of the Klamath County
Economy
(1)
Sector
2. Agricultural Services ,
5. Lodging
7. Service Stations
8. Construction
10 . Product-Oriented
11. Service-Oriented
12. Communications & Transportation
13. Financial
15. Resorts & Marinas
(2)
Output
multiplier
,. 1.82
. . 1.28
.. 1.43
.. 1.96
,. 1.47
. . 1.70
.. 1.20
.. 1.39
. . 1.08
.. 1.18
.. 1.22
.. 1.07
.. 1.15
.. 1.51
.. 1.50
.. 1.13
.. 1.29
(3)
Income-
Output
coefficients
.55
.18
.41
.43
.49
.50
.19
.35
.57
.23
.44
.31
.30
.21
.28
.20
.71
(4)
Income
multiplier
1.66
1.71
1.43
2.83
1.32
1.45
1.25
1.38
1.04
1.30
1.18
1.09
1.19
2.11
1.78
1.19
1.11
where
the value of purchased labor services from the
Household sector by the J* sector, per dollar
of total output in the j sector; that is, it
is the a. row
-------
For example, the income-output coefficient for the Agriculture sector
(H1 ) is calculated as follows :
Hl = a19x + a!92 (r21} + a!93 (r31> + + a!917
-------
of a sector must increase to obtain the desired one-dollar change in
income for that sector.
Estimation of Recreational Expenditures
To estimate the local benefits attributable to recreational activities
at Klamath Lake as it exists at the present time, the quantity of recrea-
tional expenditures that were made in the county during 1968 had to be
estimated. The data collected from re creationists at Klamath Lake, to
estimate the recreational demand model for the lake, were also used to
determine the type and magnitude of recreational expenditures made in
Klamath County. Only those questionnaires completed by recreationists
who stayed at Klamath Lake less than 20 days were used. There are 43
such questionnaires.
Travel Cost
The relevant travel cost for this analysis is all purchases made in Klam-
ath County by recreationists while traveling to and from Klamath Lake
during 1968. Travel cost is composed of six categories: Automobile,
Cafes and Taverns, Grocery, Lodging, Camping, and "Other" costs.
To estimate the travel costs incurred in Klamath County, the 43 question-
naires were put into one of two groups. The first contains those recrea-
tionists who were residents of the county, while the second included the
non-Klamath County residents. The first group contains 29 of the 43 ob-
servations. It is assumed that all travel costs incurred by the first
group were spent in the county, since the origin and destination were
both in the same county. Automobile expenses for this group were com-
puted by multiplying the number of miles traveled to and from the site
by an average cost per mile of five cents. All other components of travel
cost were estimated from data contained in the questionnaire. All com-
ponents of travel cost for the resident group were divided by the number
of people in the party to obtain the desired estimate of average travel
cost per person.
A different procedure had to be developed for the non-resident group. It
could not be assumed that all expenditures associated with traveling to
and from the site would be made in Klamath County. However, since the
questionnaire indicated where the recreationists came from, it was pos-
sible to estimate the total miles traveled in the county. The number of
miles traveled inside the county was then multiplied by 5 cents to esti-
mate automobile travel expenses incurred within the county.
An additional step was required to estimate the other five components of
travel cost for the non-resident group. The number of miles traveled in
Klamath County was divided by the total miles traveled during the trip
to obtain the percent of the total distance that was traveled within the
county. These percentages were then applied to the other components of
travel cost to estimate the amount that was spent in the local economy.
That is, if the distance traveled inside Klamath County was 10 percent of
87
-------
the total distance, it was assumed that 10 percent of the total expendi-
tures for food, lodging, and so forth was made inside Klamath County.
It was again necessary to divide these estimates by the number of people
in the party, to obtain the average travel cost per person. Table 13,
Column 2, shows the average amount per person spent inside the county for
each of the components of travel cost.
Table 13. Average and Total Travel Cost Incurred in
Klamath County, by Component, in 1968
(1)
Component
Other
TOTAL
(2)
Average
travel cost
, ... $ .6371
, ... .1088
, ... .6360
, ... .2477
. .. .0458
.1242
, ... $1.7996
(3)
Total travel
cost
$ 93,329
15,938
93,168
36,286
6,709
18,194
$263,624
It should be emphasized that the average travel cost computed here is not
the same as that computed earlier. The previous estimate ($6.84) is
larger than the one computed here ($1.80). The primary reason for the
difference is that the estimate used here represents only those travel
costs incurred in Klamath County, while the other figure represents total
travel expenditures, without geographical reference.
The estimated average travel cost incurred in Klamath County was multi-
plied by the number of people visiting the site in 1968, to estimate the
total amount of travel expenditures made in the county during the year.
The U.S. Forest Service estimates that 146,491 people visited Klamath
Lake in 1968. Therefore, recreationists spent an estimated $263,624
(146,491 x $1.7996) in Klamath County while traveling to and from Klamath
Lake. A breakdown of this cost into its components is given in Column 3
of Table 13.
On-Site Costs
An estimate of the average on-site cost per person per day was computed
in a manner similar to the travel costs discus: ed in the previous section.
88
-------
Since it can be assumed that all on-site purchases were made in the county,
it was not necessary to separate the observations into the local- and
non-local-resident groups.
There is one difference between estimating travel costs and estimating
on-site costs. Travel costs are estimated on a per-person basis, while
on-site costs are estimated on a per-person per-day basis. That is, the
various components of on-site cost are divided by the number of visitor-
days the party stayed at the lake. On-site costs are computed in this
manner because it is hypothesized that the average number of days spent
at the site during each visit will increase as the water quality of the
lake improves. This point will be expanded upon later. Column 2 of Table
14 shows the average daily cost per person for each component of on-site
costs.
Table 14. Average and Total On-Site Cost, by Component,
for Klamath Lake in 1968
(1) (2) (3)
Average on-site Total on-site
Component
Cafes
Bait
TOTAL
cost /day
$ .2132
.2985
.3360
. 0209
.0517
1.0473
.0169
.0266
$2.0111
cost
$ 61,527
86,143
96,965
6,032
14,920
302,237
4,877
7,676
$580,377
The number of visitor-days enjoyed at Klamath Lake in 1968 is estimated
by multiplying the number of visits (146,491) by the average length of
stay per visit (1.97), as estimated in the demand model. This gives
288,587 visitor-days. An estimate of total on-site costs for Klamath
Lake in 1968 is obtained by multiplying the number of visitor-days by the
on-site cost per visitor-day. Total on-site costs are estimated to be
$580,377. Total on-site cost is allocated among its components in Column
3 of Table 14. The average on-site cost per day in Table 14 is greater
89
-------
than the value vised in the demand model, because an adjustment was not
made for food costs the recreationists would have incurred if they had
stayed at home.
On-site costs and travel costs are aggregated to obtain the total expendi-
tures in Klamath County associated with recreation at Klamath Lake in
1968. Thus, $844,001 represents the total annual cost incurred in Klamath
County by recreationists at Klamath Lake in 1968, given the present water
quality of the lake. Table 15 shows how much of the total figure was
spent in the various sectors of the economy. This was determined by assign-
ing each component of travel cost and on-site cost to the appropriate sec-
tor of the model.
Table 15. Total Recreational Expenditures and Percentages,
in Klamath County, by Sector, Associated with
Recreation at Klamath Lake in 1968
(1) (2) (3)
Percent of total
recreational
Sector Expenditures expenditures
TOTAL .....
... $403,658
75,859
187,302
132,292
12,811
25,370
. .. $837,292
48.21
9.06
22.37
15.80
1.53
3.03
100.00
It should be noted that the total estimated in Table 15 ($837,292) does
not equal the sum of the totals in Tables 13 and 14 ($844,001). The
difference ($6,709) is due to camping fees incurred in Klamath County
while traveling to and from Klamath Lake. It is assumed that these camp-
ing fees were paid to the state or federal government, and not to any of
the sectors of the local economy. However, camping fees incurred while
at the site were allocated to the Resorts and Marinas sector, since all
camping facilities at the site are privately owned.
Note that only six sectors of the economy are directly affected by recrea-
tional expenditures. Column 3 of Table 15 shows the percentage of the
recreational expenditures that each of the six sectors received. The
90
-------
Service Stations sector received almost half of the total recreational
expenditures made in the county.
The Impact of Recreational Expenditures in 1968
Input-output projections are based on Equation (68). The first step is to
project a new level of final demand that is expected to occur due to an
exogenous force acting upon the economy. The new "projected" level final
demand is post-multiplied with the R matrix to obtain the new projected
total output of each sector:
X = (R) (Y)
s\
where Y = projected final demand vector,
/\
X = projected total output vector,
R = (I-A)"1 matrix.
The expenditures that recreationists at Klamath Lake made in 1968 are
viewed as a change in final demand in the input-output model. The in-
crease in recreational expenditures are multiplied through the model to
estimate the total effect of recreational expenditures associated with
Klamath Lake in 1968. The projected increase in final demand is listed
in Column 2 of Table 16, while the projected total output is listed in
Column 3 of Table 16.
Although only six sectors are directly affected by recreational expendi-
tures, all sectors in the economy are indirectly affected. This provides
an illustration of the importance of the from-to model in the study. If
the relationships between the various sectors of the economy had not been
specified, the total effect of the recreational expenditures would have
been underestimated.
The increase in household income resulting from recreational expenditures
at Klamath Lake is also estimated. Earlier it was noted that the a^ 's
of the direct coefficients matrix specify the amount that household in-
comes of that sector will increase if the output of the sector increases
by one dollar. Therefore, the increase in household income is determined
by multiplying the estimated increase in output of a sector by the a^ of
that sector. The results are listed in Column 4 of Table 16. It is esti-
mated that county household income in 1968 was $227,000 higher as a result
of the recreational activities at Klamath Lake.
91
-------
Table 16. Projected Increases in Final Demand, Total Output,
and County Household Income, by Economic Sector,
Associated with Recreation at Klamath Lake in 1968
(1)
Sector
(2)
Proj ected
final demand
/\
(Y)
(3)
(4)
Projected
total output Projected increase
(X) in household income
1. Agriculture $ 0
2. Agric. Services... 0
3. Lumber 0
4. Manufacturing &
Processing 0
5. Lodging 132,292
6. Cafes & Taverns... 75,859
7. Service Stations.. 403,658
8. Construction 0
9. Professional
Services 0
10. Product-Oriented.. 25,370
11. Service-Oriented.. 0
12. Communications &
Transportation. 0
13. Financial 0
14. Grocery 187,302
15. Resorts &
Marinas 12,811
16. Automotive... 0
17. Local Gov't 0_
TOTAL $837,292
$ 25,870
4,832
2,167
44,736
132,302
75,869
457,144
7,916
1,440
102,841
14,111
29,275
6,527
197,732
12,843
11,936
10.644
$1,138,185
$ 8,633
507
618
6,921
48,629
23,974
69,520
2,024
796
18,370
5,226
8,437
1,637
19,674
1,992
1,998
6.811
$227,767
92
-------
SECTION X
j
ECONOMIC BENEFITS OF WATER QUALITY IMPROVEMENT
In Section VI the demand model for Klamath Lake was estimated for the
existing water quality regime. The net economic value of the lake in
1968 was estimated to be about $82,000. The regional benefits associated
with recreation at Klamath Lake in 1968 were also estimated by using the
input-output model of Klamath County. Household income in the county in-
creased an estimated $227,000 as a result of recreation at Klamath Lake
in 1968. Now consider the effects of improving the characteristics of
Klamath Lake.
An Improvement in Water Quality
A possible improvement in the water quality of Klamath Lake might consist
of two steps. The first step would be the removal of the blue-green algae,
while the second would be decreasing the water temperature and improving
the beaches around the lake.
It is hypothesized that the proposed improvements will affect the use-
intensity ratings of the lake, since the lake would be better suited for
the various recreational activities. For example, the removal of algae
(Step 1) would increase the use of the lake for boating and water-skiing,
while lower water temperatures and improved beaches would increase swim-
ming and fishing at the lake. Table 17 shows the hypothesized use-intens-
ity ratings associated with Steps 1 and 2 described above. The use-intens-
ity ratings for Steps 1 and 2 were estimated by personnel at the E.P.A.
Pacific Northwest Water Laboratory in Corvallis, Oregon.
Table 17. Hypothesized Use-Intensity Ratings for Klamath Lake
at the Present Time, and after Steps 1 and 2
Klamath Lake Use-Intensity Ratings
Activity Present Step 1 Step 2
0
1
1
1
1
3
3
2
3
3
3
3
One other possibility has to be considered: Will improvements in water
quality affect any of the other variables in the demand model? That is,
93
-------
will the average on-site cost, travel cost, or income of recreationists
change as the characteristics of the site improve? To determine this, the
average values of p. , k, and y for each lake were computed and regressed
against the site characteristics. The site characteristics were represented
by summing the swimming, boating, water skiing, and fishing use-intensities
for each lake. The three equations are:
p. = 1.638 + .066Q R2 = .507 (71)
1 (.046)
k - 12.075 + .475Q R2 - .519 (72)
(.323)
y - 5,031.295 + 529.637Q R2 - .743 (73)
(220.150)
where Q represents the sum of the use-intensities of each lake.
The sample data suggests that the average values of p, , k, and y increase
as the sum of the use-intensities of a lake increase. However, the R for
each equation, and the coefficients of Q in each of the three equations,
are not significant at t'-e 10 percent level. Therefore, no relationships
between Q and the p., k, and y variables are assumed to exist. Any im-
provements of water quality will enter the demand model only through the
W and F variables.
Demand Model for Klamath Lake (Step 1)
After removal of the algae from Klamath Lake, the estimated demand model
is:
k* = 44.151 + .002y + 10.435? (74)
p* - 10.060 + ,269k - .004k2 + .000000017y2 (75)
m e.759 - .0064k* + .0064k + .0637p* - ,0637p. (?6)
The estimated average critical travel cost and average critical on-site
costs are $90.38 and $12.07, respectively. Introducing these averages
into the q^ relation, and holding k at the average value estimated prior
to Step 1, the demand function is estimated to be:
.993 - .0637?.. ,__.
e Kl (77)
The difference between this demand function and one previously derived
for Klamath Lake is the larger constant term. Thus the demand curve has
shifted to the right, indicating that the length of stay per visit has in-
creased. The demand curve is presented graphically in Figure 13. The
average length of stay per visit has increased from 1.97 to 2.41 days.
Note that the average on-site cost is the same value that was used in the
previous demand model for Klamath Lake.
94
-------
$12.07
$1.84
e'993 - '°637 PI
1.25 2.41 x
Figure 13. The Average Recreationist's Demand Curve, Per
Visit, for Klamath Lake (Step 1).
95
-------
The value per visit is estimated to be:
12.07
Value per visit = j (e'"3 " '0637Pi) d?1 - [(10.23) (1.25) ] (78)
1.84
= $18.29 - $12.79 - $5.50.
Before the net economic value of Klamath Lake, after Step 1, can be de-
termined it is necessary to estimate the number of visits to Klamath Lake
after the algae has been removed. Substituting the larger values of W
and F into the visits equation gives an estimate of 234,386 visits. This
represents a 60 percent increase in the number of visits.
The estimated net economic value of Klamath Lake, after removing the algae,
is:
($5.50) (234, 386) = $1,289,123.
The estimated value of Klamath Lake as it now exists is $82,035. The value
of removing the algae is represented by the difference in the two estimated
values, or $1,207,088. That is, based on 1968 data, $1.2 million worth of
recreational benefits could be obtained per year by removing the algae
from Klamath Lake.
Demand Model for Klamath Lake (Step 2)
It is hypothesized that lowering the water temperature of the lake and im-
proving the beaches would cause the swimming use-intensity to rise from low
to high, and the fishing use- intensity to increase from medium to high.
Again, it is assumed that all other variables are unaffected by the pro-
posed improvements. Substituting the higher use-intensity ratings into
the model yields the following demand model for Klamath Lake after Step 2:
k* = 60.426 + .002y + IQ.MSp (79)
P1 - 14.250 + .269k - .004k2 + .000000017y2 (80)
m e.759 - .0064k* + .0064k + .0637p* - .0637p1 (81)
* *
The k and p functions have again shifted, representing an increase in
the average k* and p. for recreationists at Klamath Lake. The revised
averages are $106.65 and $16.26 respectively. The proposed revised de-
mand function is :
,x - e1'156 - -0"7"! (82)
The demand function has again shifted to the right, since the constant
term is larger.
96
-------
The value per visit to recreationists at Klamath Lake after Step 2 is seen
more clearly with the use of Figure 14. The per-visit value is:
16.26
Value per visit = J (e1'156 ' -0637Pi) dp[ _ [(14.42)(1.13)] (83)
1.84
- $26.72 - $16.30 = $10.42.
When the higher use-intensity ratings are substituted into the visits
equation, the number of visits to Klamath Lake after Step 2 is estimated
to be 377,947, a 158 percent increase above the number of visits estimated
for Klamath Lake in 1968. The estimated net economic value of Klamath
Lake after the completion of Step 2 is:
($10.42)(377,947) = $3,938,208
The total increase in economic value of Klamath Lake after completion of
Steps 1 and 2 is $3,856,173. That is, the recreational benefits available
to society would be worth $3.86 million annually if the two-step improve-
ment in Klamath Lake were undertaken. $1.2 million worth of benefits
would be associated with the first step. An additional $2.66 million are
related to the second step.
Increase in Recreational Expenditures
The demand estimates of the number of visits and the length of stay per
visit are used to estimate the net increase in expenditures associated
with recreation at Klamath Lake as water quality improves. The net in-
crease in travel costs is estimated by multiplying the averages in Table
13 by the net increase in the number of visits to the site resulting from
water quality improvements. That is, upon completion of Step 1, the esti-
mated number of visits to the lake would increase from 146,491 to 234,947.
Therefore, the net increase is 87,895 visits. This figure is multiplied
by the averages in Table 13 to obtain the estimates in Column 2 of Table
18. The same procedure is used to estimate the net increase in expendi-
tures associated with Step 2 (Column 3, Table 18). (See page 90 for an
explanation of the deletion of camping fees in Table 18.)
The net increase in on-site costs was estimated in the same manner. The
net increase in visitor-days associated with Step 1 is the difference be-
tween the number of visitor-days estimated after the completion of Step 1
and the number of visitor-days estimated for 1968:
Net visitor-days (Step 1) = (234, 386) (2. 41) - (146, 491) (1.97) (84)
- 564,870 - 288,587
276,283 visitor-days.
97
-------
$16.26
$1.84
0
1.156 - .0637
1.13 2.83
Figure 14. The Average Recreationist's Demand Curve, Per
Visit, for Klamath Lake (Step 2).
98
-------
Table 18. Net Increase in Expenditures, for Each Component
of Travel Cost, Associated with Improvements of
Water Quality at Klamath Lake
(2) (3)
Net Increase in Expenditures
Component
Cafes
Other,
TOTAL
Step 1
10,964
$154.197
Step 2
g1A7 A61
2S 1 ft^
-uj j XO.J
1A7 706
57 T?l
28,823
$406.004
Completion of Step 2 would result in an estimated net increase of 781,003
visitor-days. The net increases in visitor-days are multiplied by the
average values of each component of on-site cost listed in Table 14, to
obtain the net increase in expenditures for each component of on-site
cost. The estimates for Steps 1 and 2 are listed in Table 19.
Table 19. Net Increase in Expenditures for Each Component of
On-Site Cost Associated with Improvements of Water
Quality at Klamath Lake
(1)
Component
TOTAL
(2)
Net Increase
Step 1
$ 58,904
82,470
92,831
5,774
14,284
289,351
4,669
7,349
$555,632
(3)
in Expenditures
Step 2
$ 166,510
233,129
262,417
16,323
40,378
817,944
13,199
20,775
$1,570,675
99
-------
Impact of Recreational Expenditures (Step 1)
The increase in expenditures of recreationists represents an exogenous
change in the local economy. That is, the increase in expenditures is
caused by a postulated change in the recreation experience at Klamath
Lake. This change does not alter the structure of the local economy.
Therefore, the appropriate way to view the increase in recreational ex-
penditures is as a change in the final demand of the model.
Column 2 of Table 20 is the projected final demand associated with the
removal of the algae from Klamath Lake. The projected final demand is
post-multiplied by the (I-A)~ matrix to determine the direct and indirect
increase in sales resulting from the completion of Step 1. The projected
output of each sector is listed in Column 3 of Table 20.
The total increase in output associated with Step 1 is $252,286 greater
than the original value of recreational expenditures. That is, the esti-
mated $709,829 spent in the economy by recreationists would generate an
additional increase in sales of $252,286 in the economy.
As the output of the local economy increases, household incomes also rise.
The exact magnitude of the increase is estimated by multiplying the change
in output of each sector by the household coefficient (a,q of the direct
J
coefficients matrix) of the sector. The results are listed in the last
column of Table 20. It is estimated that household income in the county
will increase $194,000 if the algae are removed from Klamath Lake.
Impact of Recreational Expenditures (Step 2)
The procedures described in the previous section are also used to esti-
mate the regional Impact associated with lowering the water temperature
and improving the beaches at Klamath Lake. The results are contained in
Table 21. Projected total output has increased to almost $2 million,
while county household income is estimated to increase more than a half-
million dollars per year if Steps 1 and 2 are completed at Klamath Lake.
The net impact associated with Step 2 can also be estimated. The change
in total output of the economy would increase $1,716,439. Household in-
come would increase an estimated $347,820 if Step 2 were undertaken after
the completion of Step 1.
A Limitation Restated
While Section X has developed some very specific numerical estimates of
several variables, sight must not be lost of the many limitations under-
lying these estimates. Many shortcomings, both in theory and empirical
techniques, were discussed in the earlier sections. We hasten to re-
emphasize that the final estimates which have just been presented are
subject to all of these shortcomings. Consequently, they are difficult
to interpret.
100
-------
Table 20. Projected Increases in Final Demand, Total Output,
and County Household Income, by Economic Sector,
Associated with Klamath Lake after the Completion
of Step 1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
(1)
Sector
- j ^ .
Manufacturing & Processing...
Communications &
(2) (3)
Klamath Lake (Step
Projected
final
demand
/v
(Y)
$ o
0
0
0
114,602
68,467
359,633
0
0
15,633
0
0
0
138,371
13,123
0
0
$709,829
Projected
total
output
(X)
$ 20,259
3,832
1,734
35,041
114,611
68,476
407,225
6,692
1,234
81,795
12,243
24,264
5,636
146,433
13,155
10,489
8,996
$962,115
(4)
1)
Projected
increase
in house-
hold income
$ 6,760
402
495
5,420
42,120
23,443
61,927
1,711
682
14,609
4,538
6,993
1,415
14,570
2,040
1,756
5,757
$194,638
The major limitation to the reliability of our estimates is probably re-
lated to the manner in which the predictions of changes in recreational
use of Klamath Lake were made, given the postulated two-step improvement
in water quality. It is recalled that "use-intensities" are employed in
the prediction model to relate recreational demand to changes in water
101
-------
Table 21. Projected Increases in Final Demand, Total Output,
and County Household Income, by Economic Sector,
Associated with Klamath Lake after the Completion
of Step 2
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
(1)
Sector
Manufacturing & Processing...
Product-Oriented
Communications &
Local Government
TOTAL
(2) (3)
Klamath Lake (Step
Projected
final
demand
(Y)
$ o
0
0
0
319,748
191,693
1,005,783
0
0
42,022
0
0
0
380,335
37,098
0
0
$1,976,679
Projected
total
output
/\
(X)
$ 56,008
10,606
4,803
96,877
319,773
191,717
1,138,867
18,631
3,440
226,391
34,164
67,432
15,720
402,596
37,187
29,299
25,044
$2,678,554
(4)
2)
Projected
increase
in house-
hold income
$ 18,690
1,112
1,370
14,987
117,548
65,644
173,222
4,764
1,901
40,433
12,651
19,434
3,946
40,058
5,767
4,905
16,026
$542,458
quality. A logically superior model can be developed for relating
changes in the physical characteristics of the water resource to responses
in human behavior. However, the empirical specification of these rela-
tionships could not be undertaken within the scope of this study. The
need for multidisciplinary research is clearly indicated in this area.
Failure to focus on the logical relationships between the characteristics
102
-------
of the physical environment and recreational behavior by going directly
to the "use-intensity" variables led to an inadequate specification of
the prediction model. One might interpret these variables as proxies for
the dependent variable itself. If so, one would expect the use-intensi-
ties to "explain" a considerable proportion of the variation in the de-
pendent variable. This could lead to an overstatement of the estimated
effects associated with a water quality improvement.
103
-------
SECTION XI
ACKNOWLEDGMENTS
The authors wish to acknowledge the valuable assistance provided by the
staff of the Pacific Northwest Water Laboratory of the Environmental
Protection Agency. Their input helped in the formulation stages of the
project, as well as during the actual analysis.
Appreciation is also extended to Dr. John A. Edwards, Department of Agri-
cultural Economics, Oregon State University, for helping with the formu-
lation of the theoretical demand model.
The Klamath County Chamber of Commerce also provided help by contacting
the businesses in the county, and soliciting their support for the study.
The authors also thank Dr. Russell Youmans, Department of Agricultural
Economics, Oregon State University, and Arnold Hoffman, Economist, Sys-
tems Analysis and Economics Branch, Division of Planning and Interagency
Programs, for their review of the manuscript.
The financial support of the Environmental Protection Agency, and the
assistance provided by Dr. Roger Don Shull, Project Officer, is also
acknowledged with sincere thanks.
105
-------
SECTION XII
REFERENCES
1. Bartsch, Alfred F. 1968. Director, Pacific Northwest Water Labora-
tory, Federal Water Pollution Control Administration. Eutropica-
tion Problems in Reservoirs. Seminar conducted by Water Resources
Research Institute. Oregon State University, Corvallis, Oregon,
October 17.
2. Beattie, Bruce Robert. 1970. "Economic Efficiency and Distributive
Consequences of Interbasin Water Transfers: A Framework for Analy-
sis." Unpublished Ph.D. thesis. Corvallis, Oregon State University.
146 numb, leaves.
3. Board of Governors of the Federal Reserve System. 1968. "Economic
Expansion in 1968." Federal Reserve Bulletin 54:941-952.
4. Bromley, Daniel Wood. 1967. "An Interindustry Analysis of the Im-
portance of Grazing on Federal Lands to the Economy of Grant County,
Oregon." Unpublished M.S. thesis. Corvallis, Oregon State Univer-
sity. 135 numb, leaves.
5. Brown, William G., Ajmer Singh and Emery N. Castle. 1964. "An Eco-
nomic Evaluation of the Oregon Salmon and Steelhead Fishery." Cor-
vallis. 47 p. (Oregon Agricultural Experiment Station. Technical
Bulletin 78.)
6. Cameron, Burgess. 1952/53. "The Production Function in Leontief
Models." The Review of Economic Studies 20:62-69.
7. Chenery, Hollis B. and Paul G. Clark. 1959- Interindustry Economics.
New York, Wiley. 336 p.
8. Clawson, Marion. 1959. "Methods of Measuring the Demand for and
Value of Outdoor Recreation." Washington, D.C., Resources for the
Future, Inc. 36 p. (Reprint No. 10.)
9. Draper, N. R. and H. Smith. 1966. Applied Regression Analysis.
New York, Wiley. 407 p.
10. Gibbs, Kenneth Charles. 1969. "The Estimation of Recreational Bene-
fits Resulting from an Improvement of Water Quality in Upper Klamath
Lake: An Application of a Method for Evaluating the Demand for Out-
door Recreation." Unpublished Ph.D. thesis. Corvallis, Oregon State
University. 156 numb, leaves.
107
-------
11. Guedry, Leo Joseph Jr. 1970. "The Role of Selected Population and
Site Characteristics in the Demand for Forest Recreation." Unpub-
lished Ph.D. thesis. Corvallis, Oregon State University. 378 numb.
leaves.
12. Hogg, Robert V. and Allen T. Craig. 1965. Introduction to Mathe-
matical Statistics. New York, Macmillan. 383 p.
13. Hotelling, Harold. 1947. Letter cited in U.S. National Park Ser-
vice. 1949. "The Economics of Public Recreation: An Economic
Study of the Monetary Evaluation of Recreation in the National Parks."
Washington, D.C. 36 p.
14. Input-Output Bibliography, 1960-1963. 1964. New York, United Na-
tions. 159 p. (St. STAT/Ser. m/39.)
15. Johnston, W. E. and V. S. Pankey. 1968. "Use of Prediction Models
for Corps of Engineers Reservoirs in California." In: An Economic
Study of the Demand for Outdoor Recreation: Conference Proceedings
of the Cooperative Regional Research Technical Committee, San Fran-
cisco. 1968. p. 15-47. (Report 1.)
16. Knetsch, Jack L. and Robert K. Davis. 1966. "Comparisons of Methods
for Recreation Evaluation." In: Water Research, edited by Allen V.
Kneese and Stephen C. Smith. Baltimore, Johns Hopkins, p. 125-142.
17. Leontief, Wassily W. 1936. "Quantitative Input-Output Relations in
the Economic System of the United States." The Review of Economic
Statistics 18:105-125.
18. Leven, Charles. 1961. "Regional Income and Product Accounts: Con-
struction and Application." In: Design of Regional Accounts, edited
by W. Hochwald. Baltimore, Johns Hopkins, p. 148-195.
19. Pearse, Peter H. 1968. "A New Approach to the Evaluation of Non-
Priced Recreational Resources." Land Economics 44:87-99.
*
20. Reiling, Stephen D. 1971. "The Estimation of Regional Secondary
Benefits Resulting from an Improvement in Water Quality of Upper
Klamath Lake, Oregon: An Interindustry Approach." Unpublished M.S.
thesis. Corvallis, Oregon State University. 120 numb, leaves.
21. Riley, V. and R. J. Allen. 1955. Interindustry Economic Studies.
Operations Research Office, bibliographic reference No. 4. Balti-
more, Johns Hopkins. 280 p.
22. Stevens, Joe B. 1966. "Recreation Benefits from Water Pollution
Control." Water Resources Research 2:167-182.
23. Stigler, George J. 1966. The Theory of Price. 3rd ed. New York,
Macmillan. 355 p.
108
-------
24. Stoevener, Herbert H. 1964. "Water Use Relationships As Affected
By Water Quality on the Yaquina Bay." In: Western Resources Con-
ference's New Horizons for Resources Research; Issues and Method-
ology. Boulder, University of Colorado, p. 87-99.
25. Stoevener, Herbert H. and E. N. Castle. 1965. "Input-Output Models
and Benefit-Cost Analysis in Water Resources Research." Journal of
Farm Economics 47:1572-1579.
26. Taskier, C. E. 1961. Input-Output Bibliography 1955-1960. New
York, United Nations. 222 p. (St. STAT/7.)
27. U.S. Bureau of the Census. 1967. Census of Agriculture 1964; Sta-
tistics for the State and Counties. Oregon. Washington, D.C. 367 p.
28. U.S. Bureau of the Census. 1968. Population Estimates; Estimates
of the Population of Counties; July 1, 1966. Washington, D.C.
September 27, 1968. (Ser. p-25, Nos. 401, 404, 407.)
29. U.S. Department of Agriculture. Agricultural Research Service.
1968. Food Consumption of Households in the U.S.; Household Food
Consumption Survey. 1965-1966, Washington, D. C. 212 p. (Report No.
1.)
109
-------
SECTION XIII
PUBLICATIONS AND PATENTS
Edwards, J. A., K. C. Gibbs, L. J. Guedry, and H. H. Stoevener. "The
Demand for Non-Unique Outdoor Recreational Services: Methodological
Issues.1' Pending publication as an Agricultural Experiment Station
Bulletin. Corvallis, Oregon State University.
Ill
-------
SECTION XIV
GLOSSARY
Consumer's Surplus - The difference between what a consumer actually
pays for a commodity and what he would be willing to pay rather than do
without it.
Critical On-Site Costs (PI) - The level of on-site costs at which the
recreationist is indifferent between recreating and not recreating, given
the utility function of the individual, his income, travel costs, and the
price of other goods. A change in any of these variables will result in
a change in the value of p*.
Critical Travel Costs (k ) - The value of travel costs at which the recre-
ationist is indifferent between recreating and not recreating, given his
utility function, his income, on-site costs, and the price of other goods.
A change in any of these variables will result in a change in the value
of k*.
Demand Curve - The locus of points representing the maximum amount of a
commodity the consumer will purchase at different prices in a given time
period, other things being equal.
Direct Coefficients (a 's) - The value of goods and services Sector j
must purchase from Sector i to produce one dollar's worth of output.
Income Multiplier (M, ) - The total change in household income of the
region, resulting from a one-dollar change in income of households in
the kth sector.
Income-Output Coefficients (H,) - The total change in income paid to all
households in the region as a result of a one-dollar change in the out-
put of the k^ sector.
Marginal Utility - The change in utility or satisfaction resulting from
a one-unit change in the level of consumption of a good or service.
Output Multiplier - The total change in the output of the entire economy
resulting from a one-dollar change in the output of one sector in the
economy.
Recreation Visit - The entry of any person upon a site or area of land
or water generally recognized as an element in the recreation population,
except those which are part of, or incidental to, the pursuit of a gain-
ful occupation.
113
-------
Recfreation Visitor-Day ^ Twelve visitor-hours, which may be accumulated
continuously, intermittently, or simultaneously by one or more persons
whd are not in pursuit of a gainful occupation at the recreation site.
114
-------
SECTION XV
APPENDICES
Page No.
A. Outdoor Recreation Questionnaire 117
B. Input-Output Questionnaire 123
115
-------
APPENDIX A
FIELD SURVEY QUESTIONNAIRE
OREGON STATE UNIVERSITY
July, 1968
. I'm working on a recreation survey for Oregon State University and
Hello, I'm
would like to ask you a few interesting questions if you don't mind!
1- 1 Visit lake (continue) Was the main purpose of your trip to visit this particular
2 Other purpose (DISCONTINUE) lake, or are you taking your trip for some other purpose?
2-
(AM or PM)
3-
(AM or PM)
4-
Date May I ask when yo
Time date and the appro
Date Now, when do you
Time again the date and
City/Town
Where do you live
County
county auu slate ?
State r
iu arrived at this particular site- -the
ximate time?
plan to leave this particular site--
approximate time of day or night?
at the present time--the city or town.
4a- 1 In city/town (skip to 5)
2 Suburban area (skip to 5)
3 Rural outside (ask 4b)
Do you live right in the city (town), a suburban area, or
a rural area outside of the city (town)?
4b-
1 Nearer site
2 Away from site
5-
Miles How many miles do you live out of the city (town)?
(INT: Mark whether nearer or farther away from site)
Number Including yourself, how many persons are there in your
party which is stopping at this particular place?
6-1 Immediate family
2 Other relatives
3 Unrelated individuals
4 Other (explain below)
Does your party consist mainly of your immediate family,
mainly of other relatives, or mainly of unrelated
individuals, such as neighbors and friends?
7-
Number Including yourself, how many persons are there in your
immediate family?
To help the University figure out how valuable recreation is to the state, I'd like to ask you about
your party's expenditures from your home to this, area.
g _ $ Enroute Approximately how much did your party spend for food and
liquor in cafes, restaurants or taverns while you were en-
route to this particular site? (just your best estimate)
117
-------
Here About how much will your party probably spend in
restaurants, cafes or taverns while you are stopping at this
particular site? (just your best estimate)
9- $
10- $
Home Approximately how much did your party spend for this trip
in grocery or liquor stores before you left home? (just
your best estimate?)
Enroute About how much did your party spend in grocery or liquor
stores while you were enroute to this particular site?
(just your best estimate?)
Here What do you think your party will spend in grocery and
liquor stores while you are stopping at this particular
place? (just your best estimate?)
Enroute While you were enroute to this site, about how much did
your party spend for lodging in motels, hotels, or trailer
parks? (just your best estimate)
Here What do you think your party will spend for lodging in
motels, hotels or trailer parks- while you are stopping at
this site? (just your best estimate)
11- $
Enroute How about camping fees--how much, if any, did your
party spend for camping fees while you were enroute to 7
this site? (just your best estimate)
Here What do you think your party will probably pay for camping
fees while you are here at this site? (just your best esti-
mate)
12 -
Miles How many miles, if any, did your party drive yesterday
while at this site?
___ ______ _.__ ____.~_._________._.»____.. _ ______.._____,^ _ ____________
12a - Purpose What was the purpose of your drive yesterday?
12b - Miles (If not at site yesterday) About how many miles, if any,
will your party probably drive today while at this site?
12c-
Purpose For what purpose will today's drive be for?
Now, please think of the gasoline and oil that will be purchased for your party's car and boat for this
entire trip.
13 -
% before First, about what percent of gas and oil for the car and
leaving boat was purchased for the trip before you left home ?
(just your best estimate)
% both Now, think of all the gas and oil that will be purchased
ways between home and here and between here and back home.
Approximately what percentage of the gas and oil will
be purchased between home and the time you get back
home from here, that is, both ways? (Estimate)
% at this What percent of all gas and oil purchased for the car and
site boat will you probably make while you are stopping at this
site? (just your best estimate)
118
-------
14 - 1 Yes(askl4a) Did your party bring a boat with you to this site?
2 No (skip to no. 15)
14a ~ , Gallons About how many gallons of gasoline does your boat use a
Gas day at this particular site ?
Quarts Hov/ many quarts of oil does your boat use in a day while
Oil here?
(INTERVIEWER: Refer to question no. 6. Ask question 15 series only if code 2, 3, or 4 is
circled in no. 6)
IS - 1 Mine (ask 15a) Whose car did you bring on the trip--yours or someone
2 Someone else (skip to 15b) else's in your party?
- "" -"---- ....-. -. ......
15a - $ How much, if any, did other members of your party
contribute for gas, oil and automotive expenses thus far
on the trip? .
i
iSb - $ How much, if any, have you contributed thus far to the
owner of the car for gas, oil and automotive expenses?
16 - _$ How much money, if any, has your party spent on boat
launching fees while on this trip?
17 - Thus far, we have talked about expenses for the automobile, boat, food and liquor, and for
lodging and camping fees. Can you think of any other types of expenses you have had coming
here, such as camera supplies, souvenirs, etc. (If YES) What type?
1 No
2 Yes Type _ ,
Total cost of these expenses $ ,
17a - What other types of expenses will you have while, stopping at this site?
1 No
2 Yes Type
Estimated cost of these expenses $
119
-------
18 - (HAND CARD TO RESPONDENT) Here is a list of items which either you or other members
of your party may own, which you have brought with you to this site. Looking over the list,
will you please tell me which owned items were brought with you? Do not inclue rented
items. (INT: Mark X for each item. Then ask remaining questions on your card for each X'd
ltem) Amount Paid
for Item
Items
Year
Purchased
Type & Location of
Store Where Piirchased
Maintenance
Boat
o , , .
^xU uj^jcLni jii vj CvX
Boat trailer
Fishing tackle (rod,
Camper (van, truck,
T 4- +~ "1
T
i CHL
Boat equipment not in-
cluded in price of boat
(preserver, fire extinguisher,
BH.» j
Water skiis, ropes, etc. -
Special clothing (such as
rubber boots, coats, rainwear,
avv j-in.iriiii£ a tllLo j CLC. j
Any other items ?
(If YES) What?
-
,
f
'.
120
-------
23-1 Male < 1 Under 21 years of age
2 Female 2 21-29 years
3 30-39
4 40- 49
3 50 - 59
6 60 or over Age and sex of respondent
24 - , ..-_ Site Where interview wa's taken
25 - ;_ a Telephone number of respondent.
Area Code {For verification purposes only)
X I hereby certify this interview was actually taken with the person described above, and
represents a true and accurate account of the interview.
. 1968
(Interviewer's Signature) (Date)
COMMENTS ON INTERVIEW (if any):
121
-------
19 - (HAND RENTAL CARD) Looking at this list of items, will you please tell me which, if any,
of these items you or other members of your party have rented for this particular trip? (INT:
Mark X for each item. Then, for each X'd item, ask the remaining questions on your card
for each X'd item)
Rental Rate
(Daily, Hourly,
Item Weekly)
Type G Location of
Store Where Rented
reel,
Boat
Outboard motor
Boat trailer
Fishing tackle (rod,
tackle box, etc, )
Camper (van, truck,
trailer camper, etc. )
Tent trailer
Tent
Back pack
Sleeping bag
Water skiis
Life vests
Other equipment for
boats-
Any other items?
(If YES) What?
Total Rent Expected
to Pay for Item
20- $
0 None
About how much will you spend at this site for various
baitsjust that amount that will be used at this particular
site?
21 - (HAND RESPONDENT INCOME CARD) Would you please look at this card and tell me which
one of these groups best fits your total family income before taxes for last year? Just call
your answer by letter, please.
8 (h) $11,000- $11,999
1
2
3
4
5
6
7
(a) Less than $3,500
(b)
(c)
(d)
(e)
(f)
(g)
$3, 500 -
$5, 000 -
$7,000-
$8,000-
$9.000-
$10, 000
$4, 999
$6,999
$7,999
$8, 999
$9,999
- $10,999
9 (i) $12,000- $12,999
_0 (j) $13,000- $14,999
1 (k) $15,000 - $16,999
2 (1) $17,000- $19,999
3 (m) $20,000- $24,999
4 (n) $25,000 or over
(INT: If $25,000 or over, get range from
respondent)
22 - INTERVIEWER: Mark below the type of activity the respondent was doing when you first
approached (him) (her), or the type of activity the respondent just finished doing.
Activity
122
-------
APPENDIX B
OREGON STATE UNIVERSITY
** **«_*._T_fc«AMtJ JL .j. A.
conducting a survey for Oregon State
you a few questions about your business
UJ.U XO.KE co ask you a few questions about your busines
mind. Everything you say is confidential, and the results
tor the area as a whole - not for any one person or busi-
if you
are tabulated
ness
First, may I ask what your total sales of mer-
chandise and services were during 1968. This
can be either calendar year or fiscal year,
whichever is easier for you.
0 None
What was the approximate amount of your sales
to private individuals during 1968? Do not in-
clude businesses or government - just private
consumers or individuals.
3 - $
0 None
$
Fed.
State
0 None
0 None
_City/County
During 1968, did you sell any merchandise or
services to government units outside Klamath
County? (If YES) What was the total amount of
these sales to government units outside Klamath
County?
During 1968, did you sell any merchandise or
services to government units inside Klamath
County? (INT: If NO, circle all three O's)
(If YES) What was the amount of your sales to
government units in Klamath County? What was
the amount of your sales to agencies of the
Oregon State government in Klamath County? And,
what was the amount of your sales to local city
and county governments?
4 - $ Outside What was the total amount of your sales to busi-
0 None nesses outside Klamath County in 1968? Again,
either the calendar or fiscal year?
5 - $
0 None
Inside What was the total amount of your sales to busi-
nesses inside Klamath County in 1968?
Now, would you please think, of the sales you made to businesses within
Klamath County during 1968. (HAND RESPONDENT CARD) On this card are
some types of businesses. As I read off each type, will you please
tell me the amount or percentage of your sales, if any, you made to
that type of business in Klamath County? (INT: Go through list one
at a time. There must be an answer recorded for each type of busi-
ness. If answer is "None", write in "0" on appropriate line)
6 -
123
-------
(a) Agriculture
(b) Agricultural services
(c) Lumber
(d) Manufacturing
(e) Lodging
(f) Cafes and Taverns
(g) Service stations
(h) Construction
(i) Professional services
(j) Product-Oriented wholesale & retail (unless
listed elsewhere)
(k) Service-Oriented wholesale & retail
(1) Communications & Transportation
(m) Financial institutions
(n) Grocery wholesale or retail
(o) Resorts and Marinas
(p) Auto and Trailer Sales
$_ (q) Other (Specify )
7-1. Corporation (Ask 8 & 9) Is this business a corporation, or some
2. Other (Skip to #10) other kind of ownership?
8 - $__ About how much in compensation was paid to cor-
0 None poration officers during 1968? Please include
all compensation including bonuses, profit-shar-
ing, and firm contributions to retirement.
8a -$ How much of this compensation, if any, was paid
0 None to officers outside Klamath County?
9 -$ - About how much in wages were paid to employees
0 None of the corporation during 1968? Please include
all wages including bonuses, profit-sharing, and
firm contributions to retirement.
9a -$ How much of these wages, if any, were paid to
0 None employees outside of Klamath County?
(INTERVIEWER: If you asked #8 and #9, skip now to #11. Questions
#10 and lOa are to be asked only of businesses which are not cor-
porations)
124
-------
10 - $
lOa - $
0 None
Including yourself, how much was paid in wages
to all employees of the firm during 1968?
^»,»,.».«,»» j^^,.,,,^^^_^_ ._in .___t [LI
How much of these wages, if any, were paid to
employees outside of Klamath County?
ASK OF EVERYONE
11 - $
0 No purchases
(If None, skip to
#18)
Did this business buy any new equipment, machin-
ery, buildings, or other capital items during
1968?
(If YES) What was the total amount of these
capital item purchases during 1968?
12 - $
0 None
Of the capital item purchases you made in 1968,
how much, if any, were purchased from individu-
als?
13 - $
0 None
Were any of these 1968 capital items purchased
from government units outside Klamath County?
14 - $
0 None
0 None
Fed.
State
? City/
0 None County
Were any of these 1968 capital items purchased
from government units inside Klamath County?
(INT: If NO, circle all three O's)
(If YES) What was the amount of your 1968 capi-
tal items purchased from federal government
units in Klamath County?
What was the amount of your capital item pur-
chases from agencies of the State of Oregon
in Klamath County?
What was the amount of your capital item pur-
chases from local city and county govern-
ments in 1968?
15 - $
0 None
Of these capital item purchases you made in
1968, how much, if any, were purchased from
firms or businesses outside of Klamath County?
16 - $
0 None
Of the capital item purchases you made in 1968,
what amount was bought from firms or businesses
inside Klamath County?
17 - Now, will you please think of the purchases of capital items which
you made from businesses within Klamath County during 1968. On
this card are the same types of businesses which you read before.
As I call off each type, will you please tell me the amount or
dollar percentage, if any, which was purchased from that business
125
-------
group in Klamath County? (INT: Go through list one at a time.
There must be an answer recorded for each business type. (If None,
write in "0")
$
(a) Agriculture
(b) Agricultural services
(c) Lumber
(d) Manufacturing
(e) Lodging
(f) Cafes & Taverns
(g) Service stations
(h) Construction
(i) Professional services
(j) Product-Oriented wholesale & retail
(k) Service-Oriented wholesale & retail
(1) Communications & Transportation
(m) Financial institutions
(n) Grocery wholesale & retail
(o) Resorts & Marinas
(p) Auto and Trailer Sales
(q) Other (Specify )
ASK OF EVERYONE
18 - $
Fed.
State
City/
County
(HAND RESPONDENT LIST OF POSSIBLE TAXES)
What is the approximate amount of taxes which
your firm paid to the federal government in
1968?
How much in taxes did your firm pay the State
of Oregon in 1968?
What was the approximate amount of taxes which
your firm paid to this county or to cities
within the county in 1968?
19 - $
0 No or None
Did your firm pay any taxes to states outside
of Oregon in 1968? (If YES) About how much?
19a - $
0 No or None
Did ypur firm pay any taxes to city and county
governments outside Klamath County in 1968?
(If YES) About how much?
126
-------
20 - 1. Yes (Continue with #21
2. No (Skip to #28)
Did your firm receive any interest,
rent, royalties, or dividends during
1968?
21 - $
What was your firm's total receipts from inter-
est, rent, royalties, or dividends during 1968?
22 - $
0 None
How much of these receipts, if any, were paid
to you by private individuals?
23 - $ During 1968, did you receive any interest, rent,
royalties, or dividends from government units
outside Klamath County? (If YES) What was the
total amount?
24 - $
Fed.
0 None
State
0 None
$
City/
0 None County
During 1968, did you receive any interest, rent,
royalties, or dividends from government units
inside Klamath County? (If NO, circle all three
O's)
(If YES) How much was received from federal
government? From the Oregon State government?
From this county or cities within the county?
25 - $
0 None
During 1968, did you receive any interest, rent,
royalties, or dividends from businesses outside
Klamath County? (If YES) What was the total
amount?
26 - $
0 None
During 1968, did you receive any interest, rent,
royalties, or dividends from businesses inside
Klamath County?
(If YES) What was the total amount?
(If NO, skip to #28)
27 - Again, here is a list of types of businesses in Klamath County. As
I read off each one, will you please tell me the amount or percent-
if any, which came from interest, rent, royalties, or dividends
------- (INT:
age.
from any of these types of businesses within Klamath County,
There must be an answer recorded on each line)
$_
$
(a) Agriculture
(b) Agricultural services
(c) Lumber
(d) Manufacturing
(e) Lodging'
127
-------
$ ._ (f) Cafes & Taverns
$ (g) Service stations
$ (h) Construction
$ (i) Professional services
$ (j) Product-Oriented wholesale & retail
$ (k) Service-Oriented wholesale & retail
$ (1) Communications & Transportation
$ (m) Financial institutions
$ (n) Grocery wholesale & retail
$ (o) Resorts & Marinas
$ (p) Auto and Trailer Sales
$ (q) Other (Specify )
ASK OF EVERYONE
28 - $ What was the total amount of depreciation taken
by your firm in 1968?
29- 1. Higher (Ask 29a)Was your inventory higher or lower at
2. Lower (Ask 29a) the end of 1968 than it was at the
3. Same (Skip to #30) beginning of the year?
4. D.K. or no inventory
29a - $_^ About how much (higher) (lower) was your inven-
tory at the end of 1968?
30 - X I hereby certify this interview was actually taken with the per-
son listed below, and represents a true and accurate account of
the interview.
(Respondent) (Firm) (Date)
(Phone Number) (Interviewer's signature)
FOR OFFICE USE ONLY**
Interview verified by
Date of verification
«U.S. GOVERNMENT PRINTING OFFICE:1973 514-152/1771-3 128
-------
Accession Number
W
;c( Field & Group
06 B
SELECTED WATER RESOURCES ABSTRACTS
INPUT TRANSACTION FORM
Department of Agricultural Economics, Oregon State University
Economic Benefits From an Improvement in Water Quality
J Q 1 Authors)
Reiling, S. D.
Gibbs, K. C.
Stoevener, H. H.
21
EPA, OEM, Project 16110 FPZ
Note
22
Citation
Environmental Protection Agency report
number, EPA-R5-73-008, January 1973.
23
Descriptors (Starred First) ~~~ ~~
Benefits*, recreation*, water quality*, economics*, lakes, camping,
sport fishing
25
Identifiers (Starred First)
Recreation demand, travel costs, on-site costs
27
Abstract
This report introduces and empirically tests a new methodology for estimating the
economic benefits accruing to society from an improved recreational facility. The
specific facility under consideration is Upper Klamath Lake, Oregon, which presently
has low water quality. The methodology draws upon previous work done in the evalua-
tion of recreational demand; however, it focuses upon the individual recreationist
and separates the traditional price variable into on-site costs and travel costs.
The model is used to estimate the number of days per visit the recreationist will
stay at the site as the water quality improves.
Data collected at three other lakes with varied characteristics are used to derive
a relationship between the number of visits to a site and the characteristics of
the site. This relationship is then used to estimate the increase in visits to
Klamath Lake that would be forthcoming with an improvement in water quality.
The impact of expanded recreational use of Klamath Lake upon the local economy is
also estimated through the use of an input-output model of the Klamath County
economy. .
Abstractor
Institution
WR;102 (REV JULY 1969)
WRSIC
SEND. W,TH COPV OF DOCUMENT
TO: WAT.* RESOURCES
WASHINGTON. D. C. 20240
* GPO! 1970-389-930
------- |