RECREATIONAL BENEFITS TRANSFER PROJECT
V. Kerry Smith, Principal Investigator
Department of Economics and Business
North Carolina State University
Raleigh, North Carolina 27695
EPA Cooperative Agreement
Project # CR813564
to
Vanderbilt Institute for Public Policy Studies
Vanderbilt University
Nashville, Tennessee
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950R89O05
RECREATIONAL BENEFITS TRANSFER PROJECT
TABLE OF CONTENTS
Page
Chapter 1. Introduction and Overview 1.1-1.7
V.- Kerry Smith
Chapter 2. Signals or Noise? Explaining the Variation .... 2.1-2.40
in Recreation Benefit Estimates
V. Kerry Smith and Yoshiaki Kaoru
Chapter 3. What Have We Learned Since Hotelling's Letter? ... 3.1-3.10
A Meta Analysis
V. Kerry Smith and Yoshiaki Kaoru
Chapter 4. Nearly All Consumer Surplus Estimates Are Biased . . 4.1-4.15
V. Kerry Smith
Chapter 5. Demands for Data and Analysis Induced By 5.1-5.72
Environmental Policy
Clifford S. Russell and V. Kerry Smith
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CHAPTER 1
INTRODUCTION AND OVERVIEW
V. Kerry Smith
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J.. 1
Introduction and Overview
This report summarizes the research completed under EPA Cooperative
Agreement # CR813564 entitled "Recreational Benefits Transfer Project." The
objective of -this research was to review all travel cost recreational demand
models completed between 1970 and 1986 from published and unpublished sources,
including all Master's and Ph.D. essays that could be identified and obtained.
From this literature a subset of the studies was assembled for meta-analysis.
The meta-analysis sought to develop a statistical summary of the results from
these demand analyses in order to determine the influences of judgmental and
site-characteristic variables on the consumer surplus estimates derived and to
gauge the effect of these variables on other measures of demands for recreational
sites. This project was funded under the Innovative Benefit Analysis Program
because the effort was viewed as exploratory. The primary research activities
were undertaken jointly with Dr. Yoshiaki Kaoru, currently an Assistant Social
Scientist at Woods Hole Oceanographic Institution. At the time, Dr. Kaoru was
a. graduate student in the Department of Economics at Vanderbilt University.
As the papers prepared under this agreement indicate, the research was
quite successful. Statistical summaries were developed for some 77 different
demand studies for recreational resources, and we compared the relative
importance of variables describing modeling judgments with characteristics of
the recreational sites and the activities undertaken at them. Four papers were
prepared with partial support from this Cooperative Agreement. Two of the papers
describing our approach have been presented at several universities in the United
States, as well as at Academia Sinica in Taiwan and at a National Bureau of
Economic Research (NBER) Conference on Data Needs for Economic Policy Making.
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One of the papers is to be published in a volume from the NBER conference. The
remainder are currently under consideration for publication. Two have received
preliminary indications of publication interest, pending suggested revisions.
Rather than rewriting the materials developed from the research papers in
an alternative technical format, this report is organized into four chapters
following th,is introductory chapter, which highlights the overall conclusions
of the research. Chapter 2 presents the first paper prepared from the research.
It describes the conceptual issues associated with using meta-analysis to
summarize estimates of the consumer surplus per unit of use across a diverse
range of travel cost demand studies and summarizes the findings from our
analysis. Chapter 3 focuses on a subset of the studies used for the meta-
analysis of per-unit benefit measures and considers the feasibility of
summarizing the estimates for other features of recreation demand (such as the
price elasticity). We used a subset here because it was not always possible to
estimate these price elasticities with the information reported in many of the
recreation demand studies.
Because consumer surplus and price elasticity estimates are themselves
random variables, Bockstael and Strand [1987] have emphasized the importance of
incorporating their properties as estimators Into policy analysis. Our use of
the Newey-West [1987] adjusted covariance matrix in evaluating the effects of
modeling assumptions was one reflection of this influence. Chapter 4 was an
unanticipated byproduct of the theoretical analysis of the properties of our
consumer surplus estimators. It proposes a new estimator for developing consumer
surplus estimates and evaluates it with some sampling experiments for a
particular specification of the travel cost demand model. This estimator offers
an alternative to the proposal recently advanced by Adramowicz et al. [1989] for
cases with unstable consumer surplus estimates. Chapter 5 places our findings
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in a somewhat more general context, as part of an evaluation of new data needs
for environmental policy making.
Several overall conclusions emerged from our research activities. They
can be categorized into three broad areas.
A. Conceptual Findings
Our theoretical analysis of the issues associated with measuring consumer
surplus suggested that virtually all consumer surplus estimates will be biased.
This follows because they usually involve nonlinear transformation of estimated
demand parameters. As a consequence of Jensen's inequality, the consumer surplus
estimates themselves exhibit bias even if the specification for the demand model
is correct. Specification errors in demand analysis simply compound the
difficulties raised by the nonlinear transformation. This implies that general
purpose strategies designed to focus on estimating demand models that serve a
variety of purposes or reliance on the existing literature wherein demand
analyses are developed to serve other purposes (test hypothesis, illustrate new
functional forms or estimators, or highlight the special features of a particular
data set) are not necessarily the best suited for environmental benefit
estimation. These objectives may not be consistent with deriving the most robust
benefit measures. While this general conclusion was probably recognized by most
researchers in this area, to our knowledge this point has not been specifically
made in the literature.
This point applies not only to the literature on travel cost recreational
demand models, but to all current techniques in use for measuring recreation
benefits, including the more recent random utility models, whether based on logit
or nested logit specifications. In all cases, the benefit measures involve a
nonlinear transformation of random variables, which in itself will induce bias
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in the welfare estimates. -This suggests that new research in the area should
consider the implications of modeling and estimation strategies specifically
designed to accomplish a broad range of benefit estimation tasks. Research on
the implications of bottom up versus top down estimates for aggregate benefit
measures, as well as on the development of "transferrable" models for measuring
consumer surplus (as opposed to the demand features of recreational resources),
seems highly appropriate. Equally important, as Chapter 4 illustrates, it is
possible to develop estimators designed to focus on consumer surplus measurement
instead of estimation of demand parameters. While this work is largely
illustrative, it nonetheless displays how the performance of alternative
estimation strategies can be sensitive to the features of the true demand
structure and the objectives of the analysis.
A further set of conceptual issues resulting from the research arises from
the meta-analysis. Here we found strong confirmation for systematic variation
in the consumer surplus estimates per unit of use across a wide range of studies.
This systematic variation could be attributed to both the features of the
resources involved and the modeling decisions made in estimating the travel cost
demand models for these recreational resources. Indeed, the most important
factors we found bore a close correspondence to the issues identified in the
literature as the most significant questions in modeling recreation demand.
Thus, the empirical analysis provides strong confirmation for the implicit
research agenda that has evolved in recreational demand modeling.
B. Empirical Findings
The empirical analysis suggest that it is possible to summarize both the
consumer surplus estimates per unit of use and the own-price elasticity of demand
for recreation sites across a wide range of studies. These estimated models
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include variables for the features of the recreation sites, as well as the
modeling judgments made in developing each of the demand estimates. After
adjustment for the panel nature of our sample data set, the results display a
remarkable degree of consistency and robustness across alternative
specifications. While these are not predictive equations in the sense that they
provide a mechanism for predicting the consumer surplus per unit of use that
would arise for each type of recreation site, they can be used as approximate
gauges of the plausibility of estimates derived from transfer exercises or from
specific studies for individual sites. Perhaps most importantly, they provide
a basis for judging the degree of maturity in travel cost recreation demand
models. By appraising the relative importance of judgmental versus theoretically
motivated variables, this type of analysis evaluates how much our current
estimates are influenced by factors that arise from a priori theory versus those
which represent analysts' adjustments to take account of incomplete data or
modeling assumptions required for meta-analysis.
C. Benefit Transfer Findings
In addition to the first two categories of results, the analysis also has
implications for the process of developing transferrable benefit estimates. The
most important of these implications is the demonstration that unifying
principles connect quite diverse estimates across modeling efforts and widely
varying recreation sites. Because these modeling efforts were undertaken by
different investigators at very different times with diverse amounts of
information, this is reasonably strong support for a set of unifying principles
connecting the per unit valuation measures for a wide range of recreational
resources.
The meta-analysis also forces the analyst to consider the measure used as
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the focus of an empirical summary. We considered two -- the consumer surplus
per unit of use and the own-price elasticity of demand. Either could provide
the basis for a benefit transfer analysis used in a policy evaluation.
Analysts have tended to use a. unit value approach to benefit transfer,
treating the model transfer task as one involving the development or transfer
of a per unit-value appropriate to the policy and then dealing with the number
of people and units of use affected by the policy as a separate question. By
forcing the selection of a metric for summary, meta-analysis has identified that
consumer surplus per unit of use need not be the focus for a benefits analysis.
The early benefit-cost analyses of Harberger [1971] and, indeed, current
evaluations of the effects of cost-reducing technological innovations in
agriculture (following Griliches [1957] early methodology for hybrid corn) rely
on point estimates of demand and supply elasticities. We could easily consider
the use of a price elasticities/local approximation approach to estimating the
benefits from a policy improving access to a recreation site (i.e. where the
change could be viewed as a price change).
Equally important, there is a general issue of how we wish to prepare these
summaries. Chapter 2 suggests that for well-behaved demand functions, we have
little intuition about the properties of the consumer surplus per unit to use
in judging the plausibility of differences in estimates across alternative
studies. Both conceptual and empirical research is needed here.
Finally, perhaps the most important conclusion for benefits transfer arises
from the inadequacy of the reporting standards used in most published research.
Because this is unlikely to change in the near future, a reorientation in the
research and data acquisition in support of benefit analysis for policy purposes
is clearly warranted. More specifically, policy offices need to establish groups
that summarize in a format consistent with the needs of a meta-analysis the
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findings of new empirical studies as they are available. By establishing a
consistent protocol for these summaries, it would be possible to request from
researchers at the time their unpublished or published reports become available
the companion supplementary information needed for meta-analyses. Usually these
are summary statistics for the variables used in the study, descriptions of
transformations, sample characteristics, clarifications, etc. When the study
is recent, this information is easily available from researchers, does not
require that they furnish their complete data (which may be planned for use in
future research). It is also a more manageable enterprise. After a lapse of
time and the completion of the policy task, these requests are less likely to
be responded to and, in most cases, the timing does not permit a response.
As policy analyses increasingly rely on using research developed for other
purposes and research available on the proverbial "research shelf," it is clearly
essential that analysts set up mechanisms to "define the shelf and maintain it."
With limited resources and an increasing number of policies to be evaluated, EPA
and other mission-oriented agencies have concluded that they cannot afford to
support research that does not have an immediate policy relationship. This means
they must choose the most important questions for these limited investments and
rely on information from the performing community for all the rest. While an
understandable response, it reinforces the need for research on how to archive
what is being done so it can be systematically used for future policy
evaluations. A meta-analytic approach forces the systematic collection of
information as it is developed. Examples of its use for policy issues (outside
economics) are now making the popular press. For example, the July 1, 1989 issue
of The New York Times reported the results of a study indicating a narrowing in
the traditional differences in verbal and mathematics aptitude scores between
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men and women. It was based on a. meta-analysis of different researchers' studies
of these groups' test performances over a number of years.
Increased availability of data, the extensive increase in contingent
valuation surveys for a wide range of environmental resources (see Mitchell and
Carson [1989]), and enhancements in micro-computing together make this task a
reasonably straightforward data management effort. Without this effort, benefits
transfer will remain.a haphazard and last-minute enterprise that is not fully
informed by available research. As such, it progressively will lose professional
credibility and fail to systematically learn from past experience.
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CHAPTER 1
REFERENCES
Adramowicz, Victor L. , Jerald J. Fletcher, and Theodore Grahara-Tomasi. 1989.
"Functional Form and the Statistical Properties of Welfare Measures,"
American Journal of Agricultural Economics (in press), May.
Bockstael, Nancy E. and Ivar E. Strand, Jr. 1987. "Regression Error and Benefit
Estimates'^ " Land Economics 63 (Pebruary) : 11-20.
Griliches, Zvi. 1957. "Hybrid Corn: An Exploration in the Economics of
Technological Change," Econometrica 25: 501-522.
Harberger, Arnold C. 1971. "Three Postulates of Applied Welfare Economics:
An Interpretive Essay," Journal of Econometric Literature 9 (September):
785-797.
Mitchell, Robert Cameron and Richard T. Carson. 1989. Using Surveys to Value
Public Goods: The Contingent Valuation Method (Washington, D. C. :
Resources for the Future).
Newey, Whitney K. and Kenneth D. West. 1987. "A Simple, Positive Semi-Definite,
Heteroskedasticity and Autocorrelation Consistent Covariance Matrix,"
Econometrica 55 (May): 703-708.
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CHAPTER 2
SIGNALS OR NOISE? EXPLAINING THE VARIATION
IN RECREATION BENEFIT ESTIMATES
V. Kerry Smith
and
Yoshiaki Kaoru
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June 15, 1989
Signals or Noise? Explaining the Variation in Recreation Benefit Estimates
V. Kerry Smith and Yoshiaki Kaoru*
I. Introduction
This paper proposes a new method for taking stock of what we have learned
about the benefits users derive from environmental resources. Our approach uses
econometric methods to review the literature. While we have applied this
approach to one class of benefit estimates--empirical studies using the travel
cost method to estimate the demand for specific recreation sites, it has general
relevance for gauging what has been learned by empirical research in many other
areas of economics.1
The research landscape for benefit estimation has changed dramatically in
the ten years since Freeman wrote his influential overview of the field. Freeman
described the motivation for his book as a response to a gap in the literature
on benefit estimation. As he noted, by 1979 there had been "...substantial
research effort devoted to developing a rigorous and unambiguous definition and
measure of changes in welfare at the theoretical level..." but "...relatively
little concern for translating the theoretical concepts and definitions into
usable, operational empirical techniques" (p. 15). This situation has changed,
especially for applications in the United States. Of the 77 travel cost
recreation demand studies analyzed in this paper, 61 were prepared since 1980.
Mitchell and Carson identified over 120 contingent valuation studies, most of
which were completed after 1980. A similar pattern emerges for hedonic property
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value studies: • of the 35 including information on air pollution, 30 .were
available after 1980. Certainly the increased role given to benefit-cost
analyses for evaluating environmental policies in Executive Order 12291 (issued
in February 1981) has contributed to the dramatic expansion in this literature
(see Smith [T98.4] and Office of Policy Analysis, U. S. EPA for evaluations).
Nonetheless, the available benefit estimates fall short of what is needed for
an increasing array of policy related activities (see Ward and Loomis; Naughton,
Parsons, and Desvousges). Indeed, the practice of adjusting the results from
one or more existing studies for a specific type of environmental resource and
using them to value changes in another resource has become a growing area for
research. Labeled as "Benefits Transfer," this process usually involves two
steps: (1) adjusting or transferring an estimated model (or set of per unit
benefit estimates) from the situation where it was developed to the new
application; and (2) developing an aggregate estimate for the relevant population
from per unit estimates and other assumptions. While judgment plays an important
role in both steps, it has been the principal basis for the first step. Many
of the published sources used for benefit estimates in policy analysis were not
designed to provide measures of the benefits for a change in the quantity or
quality of a resource. Rather, they were developed to introduce a new model,
test a hypothesis, evaluate the implications of specific assumptions, or
illustrate a "new" estimator. Consequently, they must be adapted for benefit
measurement. The nature of these modifications depends upon both the benefit
estimation task and the information reported in the original sources.
Our findings show a systematic relationship between the estimates and the
features of the empirical models. We found that both the type of recreation
site involved and the assumptions made in developing the empirical models were
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important to the results. We classified the variables used to describe models
according to whether they attempted to reflect specific theoretical issues
associated with individuals' recreation decisions or analysts' judgments needed
to estimate a model (e.g., selecting a functional form for the demand model or
making assumpri-ons to compensate for inadequate data). Ideally, the latter
variables would not be important determinants of the variation in benefit
estimates. We found that they are.
The specific factors found to be significant determinants of the real
consumer surplus per unit of use have direct implications for research on
households' recreation decision-making; for further uses of the travel cost
demand model; and for the practices used in transferring benefit estimates
derived from this class of models to new applications. We describe these
implications in the last section of the paper, after developing the background
for this approach in Section II and describing the data set as well as our
results in Section III.
II. The Role for Statistical Methods in Developing a Research Synthesis
A. Background
The use of statistical methods to develop a research synthesis has a long
history. Most of these applications have involved controlled experiments in
psychology, education, or the health sciences. They have focused on consistently
aggregating the results from different controlled experiments. In these cases,
the methods are motivated by the desire to avoid the subjective nature of most
research reviews. At best, the conventional literature review summarizes the
presence or absence of statistically significant effects and, in some cases,
compares the size of estimated effects. While many of these studies have
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attempted to draw some "bottom line" conclusions about what is known (as Light
and Pillemer observed), these appraisals often violate simple statistical
principles in distilling an admittedly complex array of work. Moreover, to
develop this type of summary, the reviewer usually must adapt the multiple (and
often complex) features of the studies to fit some comparable format in order
to propose a consensus judgment.
Because empirical research in economics is usually not based on
experimental data and may well report multiple models applied to a single data
base, our proposed methodology is different from that used in most meta analyses
(see Cordray). It must reflect both the modeling judgments (made because
controlled experiments are usually impossible) and the interdependent panel
nature of any sample of research results. .Fortunately, both issues can be
addressed with existing econometric methods.
Moreover, the rationale for using an econometric framework for synthesizing
the benefit estimates for environmental resources is more general. Empirical
models are combinations of prior theory and analyst judgment. That judgment
combines at least four elements: the problem or issue the empirical model seeks
to address (e.g., test a hypothesis or estimate a specific parameter or
quantity); the economic theory of behavior assumed to be relevant to the problem;
the data available to estimate the model; and the learning that accompanies
evaluating the joint effects of functional specification, variable construction,
and the results from prior model formulations in relationship to the existing
literature.
The last of these, sometimes referred to as specification searches or data
mining, has been widely criticized in the recent econometric literature. We do
not intend to repeat that discussion here. Rather, by viewing models as
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approximations, we have further motivation for using statistical summaries of
the results from existing models to evaluate the importance of such compromises
for the findings.
B. A Simple Model for Describing Recreation Demand Structure
The travel cost recreation demand model can be described as a derived
demand for a recreation site that contributes to each individual's production
of a recreational activity providing utility (see Deyak and Smith or Bockstael
and McConnell). As a rule, the specification for these models has been largely
a semantic exercise to assist in isolating the relevant arguments for a travel
cost demand model.2 We propose using this framework to describe the components
of modeling decisions that may explain the variation in consumer surplus
estimates across travel cost demand studies.
Consider a simple utility function specified in terms of the activities
a person wants to consume, Z,'s, as in equation (1).
U - U(Z,, Z, Zt) (1)
Each Z, is assumed to be produced by combining market goods, x,,'s; time,
t; and non-marketed commodities, y^'s, as in equation (2). Of course, some
activities may not use some inputs.
Z, - £, (x,,,..., x,,, t,, y, y.,) (2)
where x,,,... .x,,, - the amounts of the n marketed commodities used
in the production of Z,.
t, - the amount of an individual's time used in the
production of Z,.
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YD.--- Ymi = che amounts of the nonmarketed
commodities used in the
production of Z,.
To formally derive the implications of this model for travel cost demand models
we need to specify an individual's budget and time constraints to individual
decisions.
With each movement away from this fairly general description of the
household's choice problem, the analyst imposes more structure on the problem.
This structure can arise from observing how households make decisions or from
introspection. Assumptions about the constraints or features of the utility
function can also focus attention on specific aspects of decision-making because
these assumptions are considered to be important to the problems being addressed.
Finally, in most cases, available information dictates a set of compromises that
defines the structure of the model.
Developing a set of hypotheses for the factors that might influence benefit
estimates from travel cost models involves consideration of five types of
decisions:
(1) specifying the types of recreation sites;
(2) defining a recreation site, its usage, and the site quality;
(3) modeling the opportunity cost of time:
(4) describing the role of other sites in producing the recreation
service flows;
(5) linking the specification of the demand model to an underlying
behavioral model.
We use this general specification to consider how the answers provided for each
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issue affect one or more aspects of existing travel cost studies.
Describing the reasons for variation in consumer surplus estimates across
sites requires us to consider the rationale for all economic models. Most
economic models assume that individuals share common behavioral functions with
constant parameters, except for a set of distinguishing features (such as age
or education). This perspective implies that individuals have the same demand
function for a commodity or service. However, it recognizes that price and
income differences, as well as differences in demographic characteristics, can
lead to differences in the actual quantity each person will demand of any
specific commodity.
In principle, the same argument applies to the measure we have used to
summarize the travel cost demand estimates across studies--the consumer surplus
(CS) per unit of use (v). Unfortunately, conventional theory does not offer
clear guidance on the properties we might expect for this measure, given well-
behaved demand functions. This is easily seen by describing it more formally
in terms of a demand function, say g (P, I, d, q), with P the travel cost, I
the income, d demographic or taste variables, and q quality measures. CS/v can
be defined formally by (3):
PC
CS/v - L(P0> Pc, I, d, q) - / [g(p, I, d, q)/g(P,, I, d, q] dp (3)
P.
where P0 - current price
Pe - choke price
The estimates of consumer surplus from the literature are generally for specific
sites or derived from regional travel cost models hypothesized to describe sets
of sites in the same geographic region. To estimate CS/v requires some
specification of the variables hypothesized to influence L (.). We used the
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information reported in each study to estimate the consumer surplus per unit that
was representative for a typical user of the site and sample relevant to each
model.
1. Types gf-Recreation Sites
The first issue implies that we need a way to define the different types
of services provided by different recreation sites. Moreover, the classification
cannot stop here. An individual's valuation of a site's services will depend
on how these services are used. The household production framework recognizes
a site demand as a derived demand. Thus, both sources of variation must be
considered. Unfortunately, our experience with such taxonomies is quite limited.
Clawson and Knetsch classified recreation sites into three categories--
user-oriented, intermediate, and resource-based. The first type of site included
city and county parks, golf courses, tennis courts, swimming pools, playgrounds,
etc. Intermediate sites were federal and state reservoirs and parks that provide
hiking, camping, fishing, boating, and hunting. The last category had national
markets because their physical characteristics were important to the recreational
activities they supported. In the Clawson-Knetsch taxonomy, these attributes
contributed to the fishing or hiking activities in ways that cause recreationists
to perceive these activities as distinctive from the same activities undertaken
in state parks.
Our specification attempts to reflect the Clawson/Knetsch perspective, but
is forced by each study's site description to be fairly rough. Our
classification allows a site to satisfy more than.one feature simultaneously.
A site with a lake may simultaneously be a state park allowing hiking and
camping. We have also attempted to identify the primary activities analysts
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indicated were associated with each site. While some overlap is inevitable,
the association between them is not perfect.
Equally important, these activity variables may also reflect the influence
of analysts' comparative evaluations of the consumer surplus estimates.
Evaluation of.empirical models can involve comparing a model's consumer surplus
estimates with results.from the past literature to gauge their plausibility.
Because most of the commonly accepted estimates of per-unit values have been for
recreational activities, these variables' contribution to our models also may
reflect the effects of informal screening rules for model selection. Examples
of the activity-based sources for recreation value estimates include the Water
Resource Council estimates of unit day values, the Sorg/Loomis review for the
Forest Service RFA process, and (most recently) the Walsh et al. update of the
Sorg/Loomis precis of the benefits per day of specified recreational activities.
2. What is a Recreation Site and How Do We Measure the Use of it?
The early travel cost literature treated sites as well-defined entities.
Because the travel cost model arose from Harold Hotelling's suggestion to
consider the visitation patterns from concentric zones around a specified site,
this can hardly be surprising (see also Clawson). More recently, in applications
to marine recreational fishing in areas with a large array of similar sites
(e.g., estuaries) or where policy requires a coordinated treatment of a large
number of similar sites (e.g, the effect of acid rain on the Adirondack Lakes),
;
the definition of what a site is has been less clear-cut. In response to the
difficulties posted by developing separate site demand models under these
conditions, several studies pool data across sites, arguing that their parameters
were approximately constant (Sutherland [1982b]) or that site characteristics
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could be explicitly incorporated into the model (Vaughan and Russell; Smith and
Desvousges [1985]).
The variables used to measure an individual's demand for a site's services
are also important in distinguishing the available models. This specification
is another example of a decision where an a priori selection of a "best" measure
is not always apparent. What is apparent, however, is that price measurement
must be coordinated with quantity measure. Some quantity measures can imply
nonlinearities in the individual's budget constraint. Defining use typically
involves two considerations--the treatment of on-site time per trip and the time
horizon for decision making. From the perspective of a season, if ytl in
equation (2) represents the use of recreation site k, we might ask if the use
of this site is to be measured as total time at the site or if trips and time-
on-site per trip should be distinguished. For many activities, the "production"
of a day of recreation is comparable to that of a longer stay. Longer trips
simply allow more of the activity (service flow) to be produced. For other
activities, this is not a reasonable assumption. Price per unit of use will
have both fixed and variable components if use-per-trip is not held constant.
Thus, the measure selected for quantity will be important to the existence of
a conventional Marshallian demand function.1 On the basis of these arguments,
we define variables that describe the measurement of use (i.e., days versus
trips) and the treatment of on-site-time in the models.
3. Opportunity Cost of Time
There are a variety of potential specifications for the constraints to
household utility maximization--technology, income, and time constraints. The
full income concept, following Becker's original usage, links time and monetary
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constraints by defining income in terms of earnings and other sources of income.
Time is assumed to be freely substituted in any use, so all uses of time have
the same opportunity costs (the wage rate). Alternatively, we might specify
different opportunity costs, using the wage rates for part-time work (see
Bockstael, Strand, and Hanemann) . Yet another possibility specifies different
time constraints and maintains that not all types of time can be substituted (see
Smith, Desvousges, and McGivney) .
Each formulation will 'have quite different implications for the implicit
price estimated for the use of a recreation site. In this example, use
corresponds to one trip to the site. In general, an individual's implicit price,
k, to use a recreation site for a fixed amount of time would be defined as:
k - cd£ + Atf£ (4)
where: d£ = round trip distance to site £.
c - vehicle operating cost per mile
i - travel time for one round- trip to site £
A - shadow price for travel time
This implicit price would vary by the location of the individual and,
potentially, by whether vehicle costs were shared. In the full income model,
A is the wage; the Cesario/Knetsch proposal treats it as a fixed fraction of the
wage; the Bockstael et al. framework maintains that A will depend on the
definition of the marginal time unit for each person and by the degree of control
he (or she) has over time allocations. In the different "types of time" model,
A becomes a nonlinear function of the wage rate and other parameters of the
individual's decision process.
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With detailed information on the time constraints, wage rates, and job
opportunities for individuals, it would be possible to test these models.
Unfortunately, the available information generally falls short of implementing
any of these frameworks. In fact, the early models based on origin zone data
preclude serious consideration of any of these approaches. Consequently, the
literature offers a selection of approximations. Because wage rates are often
unknown, they must be estimated.
The time horizon relevant for decision making is itself an issue. This
has become especially relevant to comparisons of recreation models developed
using a random utility framework. In several cases, these models seek to explain
decisions on single trips, as if each decision was independent of what has
happened earlier. This formulation implici.tly compresses the time horizon
underlying a model of individual choice, .because in most instances it describes
the problem from a single-trip perspective. Opportunity costs must be treated
differently in this context, because the choices for time uses may be more
limited with this compressed decision horizon.
Our measures of site usage and individual time allocation decisions are
exceptionally limited. Because of these limitations, analysts have usually
proposed informal rules, such as maintaining that opportunity costs are between
one-fourth and one-half the level of the wage rate (Cesario and Knetsch). Our
analysis defines variables that describe how past studies measured the wage rate
and how they described the opportunity cost of travel time.
4. The Treatment of Substitute Sites
On theoretical grounds, we have little to debate about the relevance of
substitute prices for modeling the demand for any commodity, including
-------
2.13
recreation sites. However, this is not the issue that must be addressed in
implementing a travel cost recreation demand model. As a rule, micro level
surveys include information on the respondents' judgments about their "next best
alternative."4 Thus, in practice, the issue of including substitute prices is
not clear-cut..'. It requires determining what sites are actually available and
how potential users perceive alternative sites. As Rosenthal [1987] observed,
collinearity between price measures can yield the appearance of a small role for
substitute prices.4 For the most part, past efforts can be grouped into three
alternatives: (a) excluding any consideration of substitutes (and this has been
the majority of the work); (b) formulating arbitrary indexes of existence of
substitutes using a diverse array of specifications (each with little connection
to micro theory); and (c) including a selection of substitute prices. Based on
this diversity in practice, we have defined a variable to reflect the treatment
of substitutes.
5. The Behavioral Framework and the Empirical Model
The specification of any estimating model introduces implicit restrictions
that affect how any sample of actual choices is described. Economists working
with recreation demand modeling are beginning to question how these implicit
restrictions should be selected. For example, Kealy and Bishop, Bockstael,
Hanemann, and Strand, and other authors argue that these specifications should
follow from a well-defined behavioral model, based on a specific functional
specification for either the direct or the indirect utility function. From these
authors' perspectives the "leap of faith" that often separates the theory and
empirical sections of applied papers is inappropriate. A contrasting view of
the process might suggest that because our information is incomplete, we have
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2.14
no reason to believe a complete behavioral description will be better than
starting with a "reduced-form" approximation.
An examination of the results from existing studies cannot answer this
question, because we do not know the truth. Nonetheless, by examining the
influence of the. demand specification for the consumer surplus estimates, we can
determine whether an answer is important. To examine the importance of these
types of judgments, we grouped the variables used to describe each set of
estimates into two classes--one set reflecting different (but economically
plausible) maintained hypotheses and a second describing analyst decisions where
either the economic theory does not provide guidance or limitations in the
available data require assumptions. By testing whether the second set provides
significant determinants of the consumer surplus estimates, we can gauge the
importance of these more arbitrary modeling decisions.
III. Results
Our analysis is based on a review of published articles in a wide array
of journals that included travel cost demand models, government reports, and
unpublished papers, as well as Masters and Ph.D. theses from 1970-1986. We
identified the studies by surveying all issues of the relevant journals; by
contacting economists who have developed travel cost demand models, government
agencies (e.g., the Fish and Wildlife Service, Office of Policy Analysis in the
Department of Interior, Forest Service Regional Offices and others) and the
chairpersons of departments of agricultural economics and economics for
unpublished papers and graduate student Masters and Ph.D. essays; and by
reviewing the University of Michigan microfilm listings for the abstracted Ph.D.
dissertations in resource economics. We have attempted to exclude double entries
-------
2.15
for unpublished Ph.D. theses and subsequently published articles.
We have reviewed approximately 200 studies to determine if they had
empirical estimates for travel cost recreation demand models and provided
sufficient information to estimate the Marshallian consumer surplus per unit of
use. The results reported here relate to 77 studies with either benefit
estimates or sufficient information to derive them. The Appendix lists the
studies and the range of consumer surplus estimates in real terms for those with
sufficient information to be included in our final empirical models (columns 6,
7, and 8 in Table 2). Using all 77 studies, there are 734 observations for our
analysis. However, as we discuss further below, there is not complete
information on all variables. Several studies are responsible for multiple
observations because they reported results that varied: the demand models'
functional form; the maintained assumptions; estimators; and definition for the
recreation sites. Consequently, our sample resembles a panel data set and this
feature must be reflected in how we analyze these data.
Our empirical model hypothesizes that the variation in benefit estimates
arises from the theory underlying these demand analyses together with the
practical issues that we identified earlier to be addressed in implementing it.
The variables used to explain the estimates of benefits can be classified
according to features implied by: the assumptions inherent in the behavioral
model underlying the travel cost framework, including the definitions for the
measures for quantity and own price, as well as the treatment of substitutes
(designated here by a vector of variables, X*); the specifications used for the
estimated demand function (designated by a vector of variables, X,,); and the
econometric estimator used for the model (designated by a vector, X,).
Equation (3) above defined consumer surplus per unit of use for a given
-------
2.16
recreation site. In formulating hypotheses concerning the effects of each class
of variables on estimates of CS/v across studies, it is important to recognize
that the features of each recreation site (Xs) and the recreational activities
undertaken (XA) should influence the true value for consumer surplus per unit.
Moreover, differences in the assumptions made for the variables in L( . ) across
studies will contribute to variations in estimates of CS/v. Assuming differences
in these specifications for other economic and demographic variables are not
important, the true surplus might be hypothesized to be a function of variations
in Xj and X, as in equation (5) below. The only specification for the demand
function which satisfies this condition is the semi-log form. If b designates
the absolute value of the price coefficient, then 1/b is often used as a measure
of the Marshallian consumer surplus per unit of use (i.e. depending on how the
quantity variable for the model is defined).7
To the extent economic and demographic assumptions are greatly different
for the same type of site across studies, then we would expect a0 to vary with
them. Equation (5) assumes that each type of site and primary activity can be
classified into the categories identified by the sets of variables included in
Xj and XAI with the subscript i used to designate each estimate.
(CS/v)T1 - o, + O.X,, + aA XAI (5)
(CS/v)T is measured per unit of use to reflect differences in the conditions of
access across studies. This formulation implicitly assumes the average consumer
surplus per unit of use should be comparable (for the same types of resources,
uses, and individuals) when the conditions of access are comparable.
Estimates of (CS/v)T will be functions of demand parameter estimates, as
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2.17
well as the variables determining individual demand. Because these estimated
parameters can be shown to be functions of the true values of the parameters,
it is reasonable to hypothesize that the estimated consumer surplus per unit of
use, (CS/v)e is some function of (CS/v)T. Our proposal for summarizing empirical
work implicitly" maintains that there are more factors involved--the variables
describing each study's maintained behavioral assumptions (Xa) , as well as each
analyst's judgments (Xo and Xe). Equation (6) hypothesizes that these effects
are additive influences to the true value and therefore would be reflected in
the bias in any estimator for (CS/v)T. Linearity is a simplification.
Equation (6) has no intercept because we hypothesize that there is no fixed
bias, independent of the modeling assumptions, in the estimates for consumer
surplus per unit. The fixed bias will depend on the model used. Of course,
variables may well be omitted, but these are more likely reflected in the error
term, e,, because they can be expected to vary with each study.
(CS/v),, - /3(CS/v)T1 -I- 7Z, + .e, (6)
where Z, - a vector of variables describing modeling decisions
(i.e. Z, - (X,, XB, Xt,) with 7 a conformably dimensioned vector of
parameters
«, - stochastic error
Substituting (5) into (6) we have the basic form of our estimating model in
equation (7).
(CS/v)(l - 0a0 + fia.Xu + 0aAXA, + tZt + «, (7)
Under ideal conditions ft would be unity.
-------
2.18
An important byproduct of an attempt to model the results of applied
economic research is the development of hypotheses for the components of Z,.
This process requires reconsidering the logical structure that we assume
describes the development of economic models. While some progress has been made
in macro-economic, time-series applications (see Hendry), few findings are
available to use for applications to environmental resources. Thus, our-
discussion will be an informal first-step toward the more comprehensive efforts
required if we are to use meta-analysis in evaluating and improving applied
economic methodologies.
Following Hendry, if we regard any economic model as a strategy determined
by the problem at hand and the information available, then we can be reasonably
confident that some elements of modeling decisions (such as the treatment of
substitutes or the specification of the opportunity cost of time) should play
a role in the "true" demand function for a recreation site. But we cannot
specify in advance which of the available assumptions is correct. Moreover, we
may expect this judgment to change depending on the application. Thus, we can
distinguish studies that fail to recognize these factors from those that do, but
we cannot specify a best strategy for each case.
In applications of meta-analysis in other disciplines, these judgments are
used to develop quality weights. These weights are applied to the results from
each study as part of the development of the statistical aggregate. We have not
used this approach in our econometric analysis for two reasons. First, and most
importantly, the correct treatment of these modeling judgments in a statistical
summary depends on whether we believe they affect the bias or variance in the
estimates. Weighting implicitly assumes that the estimates based on incorrect
modeling judgments remain unbiased but simply have less informational content
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2.19
(i.e. have higher variance). While this may well be -appropriate for summaries
of studies involving primarily controlled experiments, it does not seem as clear-
cut for economic applications.
Second, because several decisions can be identified as reflections of
specific maintained hypotheses in each study, weights for each (even if the first
issue favored weighting) require a set of subweights for each of these decisions.
We do not feel this is possible given our current level of understanding of how
people make recreation decisions. Indeed, our empirical analysis provides the
first evidence on how influential these judgments are for the existing estimates.
With this background, we can distinguish variables that are largely data-
based decisions where there is little guidance available in economic theory
(those in Xo and XE) from those that are based on theory (X,). By testing the
influence of the former on our statistical summaries, we can provide some direct
evidence on the role of these types of decisions on the existing estimates. From
the perspective of transferring model results, we would prefer that these types
of decisions had a small role in explaining the (CS/v) estimates for comparable
recreation sites.
Table 1 defines the specific variables used in our analysis. (CS/v),, is
measured by the real (constant dollar) consumer surplus per unit of use. As one
would likely expect, most of our variables are qualitative. Because (CS/v),, is
derived from empirical models based on quite different data sets and precision
in estimating the parameters relevant to the estimation of the consumer surplus,
it is reasonable to expect heteroskedasticity. Indeed, as Bockstael and Strand
observed, it should be possible to estimate the variances in these estimates for
the consumer surplus. There are two potential problems with implementing this
approach. First, the information routinely reported in travel cost demand
-------
2.20
studies is generally not sufficient to construct approximate estimates of the
variances for the (CS/v) estimates. Second, and equally important, recent
sampling experiments and bootstrap calculations indicate the approximations used
in constructing these estimates can themselves be subject to important errors
(see Smith [1989] and Kling and Sexton).
The panel nature of our data set introduces another source of non-spherical
errors. If, for example, we assume a simple random effects model, then
autocorrelation will be present. In this case, it arises because there is a
common error shared by results from different models reported within the same
study. In principle, we might also want to distinguish (in the formulation used
for the error process) whether the different estimates reported for each study
reflected different modeling assumptions for the same site, the same basic model
applied to different recreation sites, or some combination of these effects, as
might be present in the regional travel cost models.
An estimator that accounts for the composite effects of all of these
factors would require imposing considerable prior information to estimate the
relevant variances and covariances for the estimates of (CS/v)e, across studies.
To avoid imposition of largely arbitrary assumptions, we have adopted an
alternative strategy--estimate equation (7) with ordinary least squares (OLS),
but report the Newey-West version of the White consistent covariance estimator
for OLS in the presence of heteroskedasticity and a generalized form of
autocorrelation.* As the results in Table 2 indicate, our basic conclusions
are largely unaffected by the standard errors used in tests of the effects of
individual variables.
Table 2 reports our estimates for several alternative models describing
the factors influencing the real consumer surplus. The numbers in parentheses
below the estimated coefficients are the t-ratios calculated with the OLS
-------
2.21
standard errors, while those in brackets are the t-ratios using the standard
errors from the adapted White consistent covariance matrix. Eight models are
reported to illustrate different aspects of our summary. The first three ignore
the role of recreation activities and focus exclusively on either assumptions
variables (column (1)) or the variables describing the type of site (column (2))
or both (column (3)). Column (4) expands the analysis in column (2) to include
the primary recreational activities supported by the site. Columns (3) and (5)
treat the definition of site type and primary recreational activities as
alternative proxies for the same effects, and include one of the two sets with
the other variables describing the modeling strategies. Columns (6) and (7)
report our most detailed model (6) and the same model omitting only the
variables describing assumptions derived largely from data-based judgments. The
last column offers an alternative to our most detailed model, deleting the
variable for the year of the data used in the study.
The variable "Year" was considered to evaluate an interesting suggestion
made by an anonymous reviewer of an earlier version of this paper. This reviewer
suggested that we might be able to investigate whether recreational resources
were growing more or less scarce by including this type of variable. Under
ideal conditions, this is an intriguing possibility. However, we believe this
variable serves primarily as a proxy variable for the composite of changes in
the types of data, estimators, and methodological advances that have taken place
over the tine period spanned by our review. These factors cannot be
distinguished from the relative value (comparable to a relative price) one would
like to evaluate for the scarcity issue. We report as "final" models equations
that include all types of effects with and without the year variable. However,
we believe that column (8) is probably a better overall description (despite
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2.22
the statistical significance of year) because of the consistency in the parameter
estimates with other less complete models and the quite consistent pattern of
change in the variables describing each study's characteristics when year is
included.
Our results have implications for three types of questions. First, because
the studies we reviewed span a period during which the conceptual models, data
sets, and estimators for recreation demand analysis improved, we can evaluate
the implications of a wide range of modeling judgments for consumer surplus (i.e.
CS/v) estimates. Second, the studies considered also include an array of
different types of recreation sites. This permits an evaluation for the relative
importance of the type of site for these estimates. Finally, they have
implications for the feasibility of using econometric reviews of the empirical
benefits literature in the task associated with benefits transfer for policy
evaluations.
It is important to recognize at the outset that the feasibility of using
econometric methods in literature reviews would be greatly enhanced with a change
in reporting conventions for empirical results. These conventions are so
variable across studies that the set of available estimates with a detailed set
of explanatory variables is almost half the size of our full sample of estimates.
Because missing values for particular classes of variables changed our sample
composition dramatically, we investigated their effects by considering
alternative subsets of the potential explanatory variables specified to influence
(CS/v). This process explains the rationale for the first five columns in Table
2. The estimated effects of the variables describing the modeling strategies
are quite stable across models in terms of their signs and statistical
significance. Virtually all the decisions on the assumptions associated with
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2.23
modeling strategies that we describe with qualitative variables were
statistically significant factors in determining the real consumer surplus (CS/v)
estimates.
When the variables are interpreted in terms of the classification we
proposed in developing equation (7), the key economic assumptions (such as the
inclusion of a substitute price or measure of the implicit costs of travel time)
are generally significant determinants of the estimate for the (CS/v) and conform
with a priori expectations. The adjustment for the measure of use indicates,
as we would expect, smaller benefits per unit in terms of days versus trips.
The parameter restrictions implicit in the use of a regional travel cost model
appear to increase estimates of (CS/v). This finding is more difficult to relate
to economic theory. The restrictions imposed by the regional travel cost model
have implications for the implicit extent of a recreation market; for whether
sites are considered equivalent (by recreationists) in terms of the estimated
demand responses to own price and income; and for the definition for what
constitutes substitute sites.
Some modeling judgments are based on each application's data and do not
have a rationale in economic theory. We have classified the variables describing
the functional form and estimator in this category. While one might argue that
the estimator follows from prior information on the sampling process, we believe
the potential sensitivity of estimates Co parameterization for the error
structure or its distribution often leads analysts to an implicit pretesting
process. In these cases, results from different estimates are compared as part
of the development of the "final" reported results. Because we have adopted this
view of the process, we have included the estimator in the data-based variables.
One way of evaluating the sensitivity of estimates to data specific
-------
2.24
judgments is to test the null hypothesis that the variables associated with
these decisions do not exert a significant influence on (CS/v). The results in
columns (6) and (7) indicate that this hypothesis is decisively rejected at the
one percent significance level.
The use "of a maximum likelihood estimator and selection of a log-linear
demand specification seem especially important individual choices. The
sensitivity of results in each case may reflect biases arising in other studies
that do not make these assumptions. This may be especially true for the use of
procedures adjusting for the on-site, intercept nature of most micro level
recreation surveys. Nonetheless, the importance of both decisions for estimates
could be reduced with improved information on the nature of households'
recreation site choices, including the amount of use and the time and resource
constraints underlying these decisions.
We are able to distinguish separate effects for our measures of the type
of recreation site and for the primary activities supported by a site. Because
the site definitions are not mutually exclusive categories, we need to interpret
the results carefully. For example, a trip to a lake in a national park would
be worth $19.94 more than one of comparable length to a coastal area (i.e., the
sum of the coefficient for National Park, 41.13, and that of Lake, -21.19 in
column (8) of Table 2). The results indicate that sites supporting wilderness
activities do not appear different than those for developed camping, comparing
their consumer surplus estimates. This seems implausible, given the activities
involved, and is likely to result from the small number of travel cost estimates
for wilderness areas (i.e. about 10 of the 399 used in the models).
Finally, this type of model offers the potential for "checking" the benefit
transfer estimates developed in policy analysis. Because we do not have a
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2.25
theoretical basis for specifying how (CS/v) should behave across different types
of recreation sites and modeling strategies, it would not be prudent to recommend
this type of model for predictions of consumer surplus per unit of use.
Intangible dimensions of a research study exist which are difficult to encode
in the quantitative terms required for an econometric summary. These factors
may well be important to how policy analysts should use a particular study in
a benefits transfer. At this stage, we can say that these types of empirical
summaries can serve as a consistency check on the processes used in policy
analyses to gauge the implications of selecting a different set of assumptions.
They also offer a first step in a more general question--how do we want to
summarize the results of applied demand analysis? Should the focus be on the
consumer surplus per unit of use or the own-price elasticity of demand? Either
could be used (with supplementary assumptions) as a basis for evaluating policy
uses of benefit studies on the research shelf.
IV. Implications
As the literature reporting benefit estimates for environmental resources
expands, the task of summarizing what we know and how to use it in evaluating
new policies that affect environmental and other resources becomes more
difficult. Our findings here indicate that econometric methods can be used to
summarize the results from diverse empirical studies. Indeed, in our specific
application (travel cost recreation demand models), this approach provided clear
support for the issues identified in the theoretical and recent empirical
literature as central to implementing the model. They include:
(a) the implications of the treatment of an individual's time constraints
for his (or her) opportunity costs of time (see Bockstael, Strand,
and Hanemann);
-------
2.26
(b.) the identification and treatment of substitute sites in modeling
recreation demand (see Rosenthal);
and
(c) the adjustment of estimates from on-site micro data sets for the
specification effects of these sampling procedures (see Shaw).
These factors are important from a conceptual perspective, and they could help
to resolve the rather wide variation in real consumer surplus across studies.
More generally, these results offer some confirmation that systematic
factors influence the disparity in results across studies. However, applied
econometric analyses of recreation demand require substantial discretionary
judgments to overcome limitations imposed by data and by our knowledge of
economic agents' behavior. Some of these factors arise from differences in the
resources involved and others from the assumptions used in these studies.
Because it appears possible to separate the influence of these factors, reviews
of empirical research using econometric methods to estimate these types of
response surfaces based on the empirical findings can also have important policy
applications. They offer a method for bounding (or for checking) the estimates
derived for new or improved resources. They can serve to identify the factors
leading to the greatest disparity in benefit estimates. And, finally, these
cross -study empirical summaries may also help to isolate the areas requiring
further research.
-------
Table 1. DESCRIPTION OF VARIABLES FOR ANALYSIS
Name
Mean
Definition of Variables
(CS/v)
SURTYPE
Type of
Recreation
Activities
Type of
Recreation Site
Substitute Price
Opportunity Cost
type #1
Opportunity Cost
type #2
Fraction of wage
Specific Site
Demand
Specifications
Year
Estimators Used*
25.24 Marshallian consumer surplus estimated per unit of use, as
measured by each study (i.e. , per day or per trip) deflated
by consumer price index (base - 1967)
.86 Qualitative variable for measure of site use - 1 for per
trip measure, 0 for per day measure
-•- Water-based recreation (swimming, boating, fishing),
hunting, wilderness hiking, and developed camping were
identified as the primary activities. The first three are
introduced as qualitative variables with developed camping
as the omitted category.
— Lake, river, coastal area and wetlands, forest or mountain
area, developed or state park, national park with or without
wilderness significance are the designations. Coastal area
and wetlands was the omitted category. Variables are unity
if satisfying designation, zero otherwise.
.29 Qualitative Variable - 1 if substitute price term was
included in the demand specification, 0 otherwise
.24 Qualitative Variable for the measure used to estimate
opportunity cost of travel time - 1 if an average wage rate
was used.
.32 Qualitative Variable for the second type of opportunity
costs of travel time measure, - 1 for use of income per
hour; the omitted category was the use of a projection for
an individual specific wage rates.
. 37 Fraction of wage rate used to estimate opportunity cost of
travel time
.24 Qualitative Variable for use of a state or regional travel
cost model describing demand for a set of sites - 1, 0
otherwise.
— Linear, log-linear and semi-log (dep) are qualitative
variables describing the specification of functional form
for demand (semi-log in logs of independent variables was
the omitted category).
— The year of the data used in each study.
--- OLS, GLS, and ML-TRUNC are qualitative variables for
estimators used, omitted categories correspond to
estimators with limited representation in studies--the
simultaneous equation estimators.
"ML-TRUNC refers to maximum likelihood estimators adjusting for truncation and
tobit estimators. GLS includes both single equation generalized least squares and
seemingly unrelated regressions.
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2.28
Table 2. DETERMINANTS OF REAL CONSUMER SURPLUS PER UNIT OF USE*
Independent
Variables
1
Intercept 20.30
(6.19)
[3.92]
SURTYPE -9.97
(-2.72)
[-1.36]
rXA) Tvr»e of
Recreation
Water-Based
Activities
Hunting
Wilderness
(Xs) Tvpe of Site
Lake
River
Forest
State Park
National Park
2
27.03
(3.68)
[3.64]
15.38
(2.97)
[2.34]
-18.69
(-3.24)
[-2.36]
-14.29
(-2.99)
[-1.95]
-18.45
(-2.36)
[-1.93]
24.95
(3.47)
[3.27]
.56
(0.04)
[0.08]
3
18.75
(0.58)
[1.04]
19.88
(3.74)
[3.55]
-20.32
(-3.52)
[-2.48]
-19.03
(-2.19)
[-1.75]
-25.99
(-3.01)
[-2.49]
22.37
(3.44)
[3.19]
-3.77
(-0.23)
[-0.13]
Models
4
23.48
(1.57)
[3.71]
14.50
(0.83)
[1.08]
17.35
(1.33)
[4.23]
-12.10
(-0.66)
[-2.49]
-17.47
(-3.12)
[-2.28]
-12.19
(-2.57)
[-1.86]
-15.37
(-1-31)
[-2.53]
14.10
(2.40)
[1.64]
30.71
(2.16)
[2.51]
5
-.30
(-.01)
[-0.01]
1.03
(0.23)
[0.12]
24.50
(1.97)
[2.72]
20.02
(1.53)
[1.63]
10.92
(0.76)
[0.62]
6
5174.24
(3.95)
[3.39]
28.75
(4.84)
[4.71]
24.43
(0.78)
[1.95]
-2.33
(-0.18)
[-0.26]
-26.57
(-1.47)
[-1.95]
-22.16
(-3.88)
[-2.57]
-16.44
(-1.91)
[-1.60]
-1.36
(-0.05)
[-0.16]
28.39
(4.28)
[3.30]
49.37
(1.33)
[1.58]
7
4904.00
(3.75)
[3.52]
16.94
(2.78)
[2.05]
-9.07
(-0.26)
[-0.96]
-1.10
(-0.08)
[-0.14]
-17.52
(-0.91)
[-1.47]
-13.21
(-2.42)
[-1.60]
3.23
(0.44)
[0.32]
-20.74
(-0.64)
[-2.25]
24.46
(3.44)
[3.07]
-5.43
(-0.14)
[-0.25]
8
-25.20
(-0.57)
[-1.74]
19.18
(3.46)
[3.10]
45.39
(1.44)
[4.01]
13.78
(1.07)
[1.46]
.60
(0.04)
[0.07]
-21.19
(-3.65)
[-2.55]
-19.80
(-2.27)
[-1.80]
6.84
(0.23)
[0.82]
22.18
(3.37)
[3.20]
41.13
(1.09)
[1.24]
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2. 29
T_able 2
Independent
Variables
fXB) Model
Assumption
Substitute Price
Opportunity Cost
Type #1
Opportunity Cost
Type #2
Fraction of Wage
Specific Site/
Regional TC Model
^TXD) Model
^Specification
Linear
Log -Linear
Semi -Log (Dep)
(XE) Estimator
OLS
GLS
1 2
-18.73
(-3.27)
[-4.58]
-14.97
(-2.10)
[-2.09]
3.95
(1.02)
[0.45]
37.24
(8.56)
[3.83]
22.23 .
(4.10)
[3.35]
Models
3 4
-13.71
(-2.12)
[-1.80]
-16.49
(-2.11)
[-2.48]
-15.86
(-3.30)
[-2.87]
48.59
(9.76)
[6.94]
24.21
(3.85)
[2.77]
-2.87
(-0.27)
[-0.31]
23.37
(2.37)
[2.88]
16.89
(1.86)
[2.97]
-14.45
(-0.48)
[-0.84]
-8.58
(-0.28)
[-0.54]
5
-23.80
(-3.76)
[-3.18]
-21.68
(-2.94)
[-2.72]
-13.59
(-2.75)
[-1.93]
55.88
(11.41)
[7.33]
21.75
(3.54)
[2.08]
12.99
(1.19)
[1.10]
28.57
(2.67)
[2.05]
15.97
(1.62)
[2.07]
-24.20
(-0.76)
[-1.39]
-24.77
(-0.78)
[-1.53]
6
-11.42
(-1.82)
[-1.43]
-6.03
(-0.73)
[-0.71]
-10.97
(-2.22)
[-1.90]
45.10
(9.09)
[6.70]
16.49
(2.55)
[1.62]
-15.33
(-1.37)
[-1.41]
15.61
(1.37)
[1.59]
9.29
(0.97)
[1.74]
-28.96
(-0.96)
[-1.39]
-21.88
(-0.73)
[-1.13]
7 8
-18.58 -14.39
(-3.00) (-2.26)
[-4.10] [-1.80]
8.03 -14.28
(0.97) (-1.75)
[0.95] [-1.98]
5.84 -15.89
(1.39) (-3.26)
[0.71] [-2.80]
27.02 48.59
(6.01) (9.76)
[2.54] [6.91]
23.54
(3.71)
[2.64]
-2.94
(-0.27)
[-0.29]
24.65
(2.36)
[2.68]
18.61
(1.96)
[2.86]
-16.21
(-0.53)
[-0.92]
-8.58
(-0.28)
[-0.53]
-------
2. 30
Table 2 (continued)
Independent
Variables
ML-Trunc
Year
R2
n
123
-67.38
(-2.15)
[-3.43]
.25 .15 .42
399 399 399
Models
4 5
-77.35
(-2.38)
[-3.65]
.15 .36
405 405
6
-85.06
(-2.74)
[-3.63]
-2.61
(-3.98)
[-3.63]
.45
399
7 8
-68.98
(-2.20)
[-3.46]
-2.47
(-3.74)
[-3.52]
.30 .43
399 399
'The numbers in parentheses below the estimated parameters are the ratios of the
coefficients to their estimated standard errors. The numbers in brackets use the Newey-West
variant of the White consistent covariance estimates for the standard errors in calculating
these ratios.
-------
CHAPTER 2 2- 31
FOOTNOTES
University Distinguished Professor, North Carolina State University, -and
Resources for the Future University Fellow; Assistant Social Scientist, Marine
Policy Center, Woods Hole Oceanographic Institution, respectively. A large
number of individuals contributed to this effort by providing the source
materials for both published and unpublished papers. Since we wrote to all the
individuals whom we could identify as active researchers in recreation economics,
and all Chairs'.of Departments of Agricultural Economics and of Economics, we
cannot identify them individually. Thanks are due Michael Hanemann for calling
our attention to the meta-analysis literature outside economics and to Peter
Caulkins, Jerry Carlson, Bill Desvousges, Ted McConnell, and three anonymous
referees for exceptionally careful and constructive comments on earlier drafts
of this paper. This research was partially supported through the U. S.
Environmental Protection Agency Cooperative Agreement No. CR812564.
1. Hedges and Olkin credit Glass with the first use of meta-analysis in
educational and psychological research. There are important differences
in the use of these methods for applications in these disciplines, as well
as for medical research, in comparison with economics. All of the former
have involved controlled experiments, where the statistical analysis can
be treated as aggregating independent observations from each study's sample
of experimental findings (see Cordray).
2. Bockstael and McConnell [1983] is a notable exception to this work, because
they use the formal structure of a household production framework to
describe the measure of the demand for non-marketed commodities and the
role of the assumption of weak complementarily.
3. This problem is analogous to the issues raised in modeling the demand for
electricity in the presence of declining block rates (see Taylor [1975]
for an early discussion) or in the more recent analyses of hedonic models'
ability to recover estimates of the willingness-to-pay functions for non-
marketed resources. See fiartik and Smith [1987].
4. These types of questions can be found on the recent Public Area Recreation
Visitors Surveys conducted by the U.S. Forest Service, as well as on a
wide variety of other micro-level site-specific surveys. This framework
presumably arises because of the difficulty of encoding (with an on-site
survey) a consistent set of substitute sites. See Smith and Desvousges
[1986] for discussion of a procedure used in surveying water-based
recreation participation patterns as part of a contingent valuation survey.
5. Hof and King [1982] give the impression that the issues are clear-cut.
In practice, data inadequacies and on-site surveys make the process of
inferring the feasible set of substitutes and of treating them consistently
exceptionally difficult.
-------
2.32
6. Collinearity in the cross price measures makes it difficult to precisely
estimate their effects on demand. It does not affect the magnitude of the
estimated coefficients. However, to the extent these are not estimated at
conventional standards for statistical significance, practitioners can
easily be faced with a dilemma in judging how to interpret and respond to
test results in these cases.
7. While this estimator for (CS/v) has been commonly used in the literature,
without a consistency check to screen for negative values, it will not have
finite moments (see Smith [1989]).
8. A lag of eleven periods was used in implementing the Newey-West version
of White's estimator.
-------
CHAPTER 2
APPENDIX
Real Consumer Surplus per Unic of Use and
Own Price Elasticity of Demand*
2.33
Ranse (Estimate)
Author
Identification Number of
Number Estimates
(CS/v)
Own Price
Elasticity
Karl C. Samples and 1
Richard Bishop
Marc 0. Ribaudo - 2
and Donald J. Epp
Donald H. Rosenthal [1985] 4
Christine Sellar 5
Cindy F. Sorg, 13
John B. Loomis, D. Donnelly,
G. Peterson, L. Nelson
Abraham E. Haspel and 17
F. Reed Johnson
Fredric C. Menz and 22
Donald P. Wilton
John K. Mullen and 23
Fredric C. Menz
William G. Brown, 25
Colin Sorbus,
Bih-lian Chou-Yang, and
Jack Richards
J. A. Sinden 34
R. E. Capel and R. K. Pandey 37
Ronald J. Sutherland (1982a) 45
V. Kerry Smith and 51
William H. Desvousges (1985)
V. Kerry Smith, William H. 52
Desvousges, and Ann Fisher
John B. Loomis (1986a) 62
John B. Loomis (1986b) 63
W. David Klemperer, 67
Gregory J. Buhyoff,
P. Verbyla, and L. Joyner
11
22
11
51
1
1
40
44
1
3
8
.11 - 6.24
3.66
.46 - 5.85
2.89 - 15.17
9.19 - 20.81
20.60 - 36.84
9.02 - 20.60
7.41 - 13.12
15.93
.29
9.26
1.36 - 40.32
1.97 - 219.78
7.21
12.53
11.53 - 22.36
.92 - 3.90
-.49
-1.79 to -4.58
•0.003 to -0.02
-1.49
-.54
-1.05
.04 to -2.99
•1.63 to -1.71
-------
2.34
Appendix (continued)
Author
Identification Number of
Number Estimates
Range (Estimate)
(CS/v)
Own Price
Elasticity
Cindy F. Sorg and
Louis J. Nelson
71
Cindy F. Sorg, 72
John B. Loomis, D. Donnelly,
G, Peterson, L. Nelson
Dennis M. Donnelly, 73
John B. Loomis,
Cindy F. Sorg and Louis Nelson
Stephen Farber 79
Werner J. Sublette and 82
William E. Martin
William J. Vaughan and 84
Clifford S. Russell
1
4
21.20 - 33.50
13.23 - 14.41
6.67 - 9.35
17.45
7.88 - 37.54
3.23 - 7.88
Thomas Gifford Sawyer
C. Tim Osborn
Trellis G. Green
Daniel Wayne McCollum
Colin Norman Sorhus
Faisal Moftah Shalloof
Bahram Adrangi
Steven Eric Daniels
Chung -Huang Huang
Margaret Tambunan
V. Kerry Smith and
Raymond Kopp
V. Kerry Smith (1975)
96
97
98
99
103
105
109
112
113
114
115
116
1
1
2
28
4
8
2
5
43
73
2
2
59
8
9
49
7
4
4
4
4
48
88
.96
.06
.23
.14
.68
.99
.93
.77
.22
5
.11
.07
- 146
- 146
- 28
- 91
- 10
6
- 60
- 327
- 11
.03
.95
.95
.47
.59
.02
.23
.20
.22
.84
-.17
-.27
-.0016 to -.005
—
-.73 to -.81
—
...
-5.97 to - 6.96
-.05 to -.84
-.0003 to -.93
-1.59 to -1.71
• » •
These results are for only those studies included in our most detailed model
based on 399 estimates from 35 studies.
-------
2.35
CHAPTER 2
REFERENCES
Adrangi, Bahram. 1982. Change in Economic Efficiency Resulting from Allocation
of Oregon National Forest Land to Skiing, dissertation, University of
Oregon, June.
Bartik, Timothy J. and V. Kerry Smith. 1987. "Urban Amenities and Public Policy,"
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Becker, Gary S. 1965. "A Theory of the Allocation of Time," Economic Journal 75
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Bockstael, Nancy E. and Kenneth E. McConnell. 1981. "Theory and Estimation of
the Household Production Function for Wildlife Recreation," Journal of
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. 1983. "Welfare Measurement in the Household Production
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Bockstael, Nancy E. and Ivar E. Strand, Jr. 1987. "Regression Error and Benefit
Estimates," Land Economics 63 (February): 11-20.
Bockstael, Nancy E. , W. Michael Hanemann, and Ivar E. Strand, Jr. 1987.
Measuring the Benefits of Water Quality Improvements Using Recreation
Demand Models. Department of Agricultural and Resource Economics,
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Bockstael, Nancy E., Ivar E. Strand, Jr., and W. Michael Hanemann. 1987. "Time
and the Recreation Demand Model," American Journal of Agricultural
Economics 69 (May): 293-302.
Brown, William G., Colin Sorhus, Bih-lian Chou-Yang, and Jack Richards. 1983.
"Using Individual Observations to Estimate Recreation Demand Functions:
A Caution," American Journal of Agricultural Economics 65 (February):
154-157.
Capel, R. E. and R. K. Pandey. 1973. "Evaluating Demand for Deer Hunting: A
Comparison of Methods," Canadian Journal of Agricultural Economics 21
(November).
Cesario, Frank J. and Jack L. Knetsch. 1970. "Time Bias in Recreation Benefit
Estimates," Water Resources Research 6 (June): 700-704.
Clawson, Marion. 1959. "Methods of Measuring the Demand for and Value of Outdoor
Recreation," Resources for the Future, Reprint No. 10, February.
Clawson, Marion and Jack L. Knetsch. 1966. Economics of Outdoor Recreation
(Baltimore: John Hopkins University).
-------
2.36
Cordray, David S. 1987. "Strengthening Causal Interpretations of Non-
Experimental Data: The Role of Meta-Analysis," unpublished manuscript to
appear in L. Sechrest, J. Bunker, and E. Perrin, ed. , Improvine Methods
in Non-Experimental Research (Menlo Park, Co.: Sage Publications).
Daniels, Steven Eric. 1986. Efficient Provision of Recreational Opportunities:
The Case of U. S. Forest Service Campgrounds, dissertation, Duke
University, January.
Deyak, Timothy"A,, and V. Kerry Smith. 1978. "Congestion and Participation in
Outdoor Recreation: A Household Production Approach," Journal of.
Environmental Economics and Management 5 (March): 63-80.
Donnelly, Dennis M. , John B. Loorais, Cindy F. Sorg, and Louis Nelson. 1985.
"Net Economic Value of Recreational Steelhead Fishing in Idaho," Bulletin
RM-9, Rocky Mt. Forest and Range Experiment Station.
Farber, Stephen. 1985. "The Value of Coastal Wetlands for Recreation: an
Application of Travel Cost and Contingent Valuation Methodologies,"
unpublished paper (October).
Freeman, A. Myrick III. 1979. The Benefits of Environmental Improvement: Theory
and Practice (Baltimore: Johns Hopkins University).
Glass, G. V. 1976. "Primary, Secondary, and Meta-Analysis of Research,"
Educational Researcher. Vol. 5, No. 1, 3-8.
Green, Trellis G. 1984. Compensating and Equivalent Variation of the Florida
Saltwater Tourist Fishery, dissertation, Florida State University, January.
Haspel, Abraham E. and F. Reed Johnson. 1982. "Multiple Destination Trip Bias
in Recreation Benefit Estimation," Land Economics 58 (No. 3, August).
Hedges, Larry V. and Ingram Olkin. 1985. Statistical Methods for Meta-Analysis
(Orlando, Florida: Academic Press).
Hendry, David F. 1983. "Econometric Modeling: The 'Consumption Function' in
Retrospect," Scottish Journal of Political Economy 30 (November): 193-220.
Hof, J. G. and D. A. King. 1982. "On the Necessity of Simultaneous Recreation
Demand Equation Estimation," Land Economics 58 (November): 547-552.
Hotelling, Harold. 1947. Letter to the National Park Service in Economics of
Outdoor Recreation--The Prewitt Report.
Huang, Chung-Huang. 1986. The Recreation Benefits of Water Quality improvement
in Selected Lakes in Minnesota, dissertation, University of Minnesota,
January.
-------
Kealy, Mary Jo and Richard Bishop. 1986. "Theoretical and Empirical Specification
Issues in Travel Cost Demand Studies," American Journal of Agricultural
Economics 68 (August): 660-667.
Klemperer, W. David, Gregory J. Buhyoff, P. Verbyla, and L. Joyner. 1982.
"Valuing White-Water River Recreation by the Travel Cost Method,"
unpublished paper.
Kling, Catherine L. and Richard J.. Sexton. 1989. "Bootstrapping in Welfare
Analysis," unpublished paper, University of California, Davis, March.
Light, Richard J. and David B. Pillemer. 1984. Summing Up: The Science of
Reviewing Research (Cambridge: Harvard University Press).
Loomis, John B. 1986. "Economic Losses to Recreational Fisheries due to Small-
head Hydro -power Development: A Case Study of the Henry's Fork in Idaho,"
Journal of Environmental Management 22 (January) .
Loomis, John B., Cindy F. Sorg, and Dennis M. Donnelly. 1986. "Evaluating
Regional Demand Models for Estimating Recreation Use and Economic Benefits:
A Case Study," Water Resources Research 22 (No. 4, April): 431-438.
McCollum, Daniel Wayne. 1986. The Travel Cost Method: Time. Specification.
and Validity, dissertation, University of Wisconsin-Madison, May.
McConnell, K. E. and I. E. Strand, Jr. 1981. "Measuring the Cost of Time in
Recreational Demand Analyses: An Application to Sport - f ishing, " American
Journal of Agricultural Economics 63: 153-156.
Menz, Fredric C. and Donald P. Wilton. 1983. "Alternative Ways to Measure
Recreation Values by the Travel Cost Method," American Journal of
Agricultural Economics 65 (May): 332-336.
Mitchell, Robert Cameron and Richard T. Carson. 1989. Using Surveys to Value
Public Goods: The Contingent Valuation Method (Washington , D . C . :
Resources for the Future) .
Mullen, John K. and Fredric C. Menz. 1985. "The Effect of Acidification Damages
on the Economic Value of the Adirondack Fishery to New York Anglers,"
American Journal of Agricultural Economics 67 (February): 112-119.
Naughton, Michael C. , George R. Parsons, and William H. Desvousges. 1988.
"Benefits Transfer: Conceptual Problems in Estimating Water Quality
Benefits Using Existing Studies," unpublished paper, February.
Newey, Whitney K. and Kenneth D. West. 1987. "A Simple, Positive Semi -Definite,
Heteroskedasticity and Autocorrelation Consistent Covariance Matrix,"
Econometrica 55 (May): 703-708.
Office of Policy Analysis. 1987. EPA's Use of Benefit-Cost Analysis:
1986 (Washington, D. C. : U. S. Environmental Protection Agency, August),
EPA-230-05-87-028.
-------
2.38
Osborn, C. Tim. 1981. "The Value of Recreational Benefits due to Controlling
Erosion in the North Lake Chicot Watershed," M. S. thesis, University of
Arkansas, May.
Ribaudo, Marc 0. and Donald J. Epp. 1984. "The Importance of Sample
Discrimination in Using the Travel Cost Method to Estimate the Benefits
of Improved Water Quality," Land Economics 60 (November): 397-403.
;;osenthal, Donald H. 1985. Representing Substitution Effects in Models of
Recreation Demand, dissertation, Colorado State University.
. 1987. "The Necessity of Substitute Prices in Recreation
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828-837.
Samples, Karl C. and Richard C. Bishop. 1985. "Estimating the Value of
Variations in Anglers' Success Rates: An Application of the Multiple-Site
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Sawyer, Thomas Gifford. 1976. "An Economic Study of the Demand for Publicly
Provided Outdoor Recreation at Beaver Reservoir," M. S. thesis, University
of Arkansas, January.
Sellar, Christine. 1982. The Value of Recreational Boating at Lakes in East
Texas, dissertation, Texas A & M University.
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-------
2.39
1986. Measuring Water Quality Benefits (Boscon: Kluwer
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-------
2.40
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838.
-------
CHAPTER 3
WHAT HAVE WE LEARNED SINCE HOTELLING'S LETTER?
A META ANALYSIS
V. Kerry Smith
and
Yoshiaki Kaoru
-------
3.1
What Have We Learned Since Hotelling's Letter?
A Meta Analysis
V. Kerry Smith and Yoshiaki Kaoru
I. Introduction
In 1947, Harold Hotelling proposed the first indirect method for measuring
the demand for,a non-marketed commodity. His letter, responding to a request
by the director of the National Park Service for methods that might be used to
measure recreation benefits, introduced the travel cost recreation demand
method1. About twelve years later, Trice and Wood [1958] and Clawson [1959]
independently implemented the methodology. Because there have been hundreds of
applications in the intervening thirty years, a comprehensive literature review
could easily fill several lengthy papers2. Moreover, given the diversity of
recreation sites and types of data, the task of developing a consistent synthesis
is exceptionally difficult.
This paper proposes the use of econometric methods for quantitative reviews
of empirical literature. Our strategy builds on the concept of statistical
review or meta-analyses introduced into the education and psychology literature
by Glass [1976] (see also Hedges and Olkin [1985] and Cordray [1987] for detailed
discussion). Because empirical studies in economics are rarely controlled
experiments, the data aggregation methods proposed for most met a analyses must
be replaced by the multiyariate methods routinely applied in econometric
analysis. This paper uses the travel cost recreation demand literature to
illustrate what can be learned from a meta-analytic review.
II. Data. Model and Results
The data for this meta-analysis of travel cost recreation demand models
were derived from a larger study investigating the feasibility of transferring
-------
3.2
recreation benefit estimates from the situations where they were estimated to
new applications of policy interest (see Smith and Kaoru [1989]). As part of
that effort, we reviewed 200 published and unpublished studies of the demand
for recreation resources prepared from 1970 to 1986. The set of studies
considered was developed by: (1) reviewing all journals (both economic and
noneconomic) that consistently publish recreation demand studies; several
computer literature searches and dissertation abstracts; and by contacting active
researchers in this area, chairpersons for all economics and agricultural
economics departments with graduate programs in the U.S., and the research
experiment stations of the U.S. Forest Service.
Seventy-seven of these studies reported sufficient information to permit
estimation of the benefits provided by the site(s) involved in each study. They
represent the initial data base for this study. Forty-seven were unpublished
(Master's and Ph.D. theses and papers or reports) and 30 published3. Seventy-
nine percent of the studies were prepared in 1980 or later. Thirty-one studies
reported sufficient information to estimate the own price elasticity of demand
implied by each demand model. Our analysis was confined to the studies whose
models yielded theoretically plausible elasticity estimates (i.e., negative
values). Overall, these studies lead to 211 own-price elasticity estimates4; 88
percent of these cases also had sufficient detail to permit a meta analysis of
the determinants of the estimated price elasticities.
Our analysis is based on a simplified view of model development adapted
from Hendry's [1983] work in the context of macro models. The arguments we
hypothesize to be the important determinants of the quantity demanded of a normal
good or service are reasonably well-defined from theory (i.e., prices, income,
-------
3.3
and perhaps variables reflecting individual tastes). The empirical
implementations of these models depend on the problem(s) being addressed and
the data available. For the most part, inadequacies in data introduce a large
number of compromises. Our specific application is important to these
compromises.
The essential element in Hotelling's proposal was the recognition that
people pay an implicit price for the use of a recreation site. This cost is the
total of the travel-related costs to visit the site, including both the vehicle-
related and time costs. The pricing of the time costs has been an important
research focus of the literature. Equally important, the definition of
substitutes for a particular recreation site and the measurement of how a site
is used are also important distinguishing features of past studies. The type
of data available affects the estimator used and has been important to the
diversity of estimates in recent applications. Theory does not offer guidance
on the functional form or definition of what constitutes homogeneous services
from one (or more) recreation site(s). In addition to these practical modeling
decisions, we would expect that demands for different types of sites would b«
different3.
On the basis of these types of arguments, we might hypothesize that
estimates of the demand parameter of interest, y, would be a function of: what
is demanded (i.e., the type of site) Xx; how the economic arguments are defined
and measured X^ and potentially some of the details of implementation X3, as in
(1)
Xi - <*o + °lXli + a2^2i + <*3X3i +
-------
3. 4
error, reflecting omissions, modeling mistakes and the approximate nature of
equation (1).
The composition of Xlf X2, and X3 will depend on what we designate as y.
Because the own-price elasticity of demand is usually a key motivation for
developing demand estimates, it seems a natural choice for y. However, it need
not be the only one. One important by-product of this process of developing
these types of empirical summaries is the identification of this issue. It is
quite possible that different model features would be statistically summarized
for different uses of the literature, i.e. , one for policy analysis, another for
classifying recreation sites, etc.
Table 1 reports the estimates for two specifications for equation (1).
The first column includes variables describing the type of site; the economic
assumptions made in developing the models and the data-based features (such as
the parameter restrictions used, functional form and estimator).
The results indicate that our empirical summary has been exceptionally
successful. The type of site and economic assumptions made do matter, as we
would expect. In interpreting the signs of the coefficients, note the own
elasticity has been entered as a negative value. Somewhat more troublesome is
the fact that assumptions without clear connection to economic theory, arising
from the data (and therefore the estimator) or the functional specification used
for the models also matter. The second column reports the results without these
variables. While the effects of the remaining variables are quite stable, we
reject this exclusion restriction based on an F-test restricting a subset of the
coefficients to zero.
Two types of test results are reported for each estimated parameter--one
based on the ordinary least squares covariance matrix and a second that
-------
3.5
recognizes the prospect for nonspherical errors. This arises because our sample
resembles a panel in that many studies report multiple estimates--either
different results for different sites or comparisons of the effects of modeling
assumptions. In both cases we might expect some correlation between the
estimates. Consequently, we used the Newey-West [1987] variant of White's [1980]
consistent covariance matrix to allow for generalized forms of both
heteroskedasticity and autocorrelation. These are reported in brackets below
the conventional t-ratios and do not change our basic conclusions.
III. Implications
Hotelling's letter offered enormously valuable advice. The travel cost
recreation demand model is now widely accepted among resource economists, as well
as in federal guidelines for benefit analysis (see U. S. Water Resources Council
[1983] and U.S. Department of Interior [1986]). It is generally regarded as a
robust methodology. ' Our findings suggest that this perception must be
interpreted carefully. While the model has been successful for a wide range of
applications in estimating plausible demand relationships for recreational
sources, a systematic analysis of the record indicates that modeling assumptions
do matter. Estimates of the own price elasticity of demand depend on how the
issues identified in the current recreation demand literature as important
theoretical questions--the measurement of the opportunity cost of time,
definition of substitution alternatives and measurement of use (i.e. using trips
or days as the dependent variable)--are resolved. They are also affected by
decisions that are often data-based with little theoretical justification.
-------
3. 6
Table 1. Estimated Price Elasticity of Demand from Travel Cost Models:
A MetaTAnalysisa
Price Elasticity of Demand
Variable
Intercept
Qualitative Variable for
Measure of Use
1 = trip 0 - per day
Qualitative Variables for
Type of Site
(Overlapping Categories)1*
Lake
River
Forest
State Park
Presence of Substitute Price
(-1)
Use Average Wage Rate to
Measure Opportunity Cost of
Travel Time (-l)e
Use Family Incoae per Hour to
Measure Opportunity Cost of
Travel Time (-l)e
Fraction of Wage Used for
Opportunity Cost of Time
Full Excluding
Specification Judgemental Variables
1033.99
(7.28)
2.11
(3.33)
-.02
(0.05)
-1.77
(-2.54)
-3.77
(-4.74)
2.28
4.28
-1.83
(-6.72)
4.25
(4.20)
1.63
(4.18)
-1.72
(-4.39)
[4.62]
[3.40]
[0.05]
[-2.38]
[-3.40]
2.97
[-5.62]
[2.98]
[3.12]
[-3.26]
829.97
(5.92)
2.45
(4.70)
-.57
(-1.36)
-1.80
(-2.27)
-4.03
(-4.61)
2.04
(3.81)
-.78
(-3.15)
3.25
(3.28)
1.12
(3.93)
-1.73
(-6.41)
[4.12]
[3.73]
[-1.35]
[-2.23]
[-4.66]
[3.56]
[-1.23]
[2.55]
[3.15]
[-4.56]
Regional Travel Cost Model
(pooled across set of site -1)
-.68
(-1.49) [-1.50]
-------
3. 7
Table 1 (continued)
Variable
Price, Elasticity of Demand
Full Excluding
Specification Judgemental Variables
Linear Demandd
(=1)
Log-Linear Demand4
(-1)
Semi-Log Demand
Dependent Variable11 (-1)
OLSa
(-1)
GLS9
(-D
ML-Truncation"
(-D
Year of the Data Used
in Each Study
n
2.39
(2.15) [2.76]
-.22
(-0.20) [-0.28]
.67
(0.55) [0.53]
.22
(0.19) [-0.30]
.35
(0.31) [0.52]
-1.44
(-1.24) [-1.77]
-.52
(-7.30) [-4.63]
.65
185
-.42
(-5.93)
[-4.13]
.45
185
"The numbers in parentheses below the estimated coefficients are the ratios
of coefficients to their OLS estimates of the standard errors. Those in brackets
use the Newey-West [1987] estimates of the standard errors allowing for a
generalized form of heteroscedasticity and autocorrelation.
bThe omitted category is coastal area and wetlands.
cThe omitted category is using a wage model to predict an individual
specific usage.
dThe omitted category is a semi-log using independent variables.
"The omitted category is a simultaneous equation estimator.
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CHAPTER 3 3i 8
Footnotes
1. Hotelling's [1947] letter originally described the method as follows:
Let concentric zones be defined around each park so that
the cost of travel to the park from all points in one
of these zones is approximately constant. The persons
entering the park in a year, or a suitable chosen sample
of'tihem, are to be listed according to the zone from
which they came. The fact that they come means that the
service of the park is at least worth the cost, and this
cost can probably be estimated with fair accuracy....A
comparison of the cost of coming from a zone with the
number of people who do come from it, together with a
count of the population of the zone, enables us to plot
one point for each zone on a demand curve for the
service of the park. By a judicious process of fitting,
it should be possible to get a good enough approximation
to this demand curve to provide, through integration,
a measure of consumers' surplus...
2. Recent reviews of this literature include Ward and Loomis [1986],
Bockstael, McConnell, and Strand [1989] and Smith [1989].
3. The classification of published and unpublished is somewhat misleading.
We used the most complete source for developing our estimates and did not include
a separate summary for a thesis that subsequently led to a published paper. In
some cases, unpublished Ph.D. theses have yielded papers after our review was
completed.
4. There have been several approaches to this problem in the literature. All
impose restrictions on the modeling of recreation decisions, based on a priori
judgments. For example, regional travel cost models restrict the demand
parameters for collections of sites in the same general area to be equal (or
change in systematic ways with specified characteristics). The varying parameter
framework is similar but uses sites drawn from anywhere in the U.S., provided
they supported comparable recreation. The random utility models identify a set
of characteristics and the group of sites assumed to comprise the choice set.
There are other formulations as well. None follows directly from theory. Each
requires a different set of assumptions about how people make recreation
decisions. Our data do not include random utility models. As of 1986, too few
studies used this framework to distinguish it from results based on more
conventional demand models.
5. The travel cost model is usually described as a derived demand for a
recreation site's services because each visitor produces recreational activities
(e.g., fishing, hiking, swimming, etc.). If we assume the household production
functions for these activities are different, then we would expect differences
in the site demands depending on the activities undertaken.
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CHAPTER 3 3>9
References
Bockstael, Nancy E. , Kenneth E. McConnell and Ivar E. Strand. 1989.
"Recreation," in J.B. Braden and C.D. Kolstad, editors, Measuring Demand
for Environmental Commodities, unpublished manuscript, University of
Illinois.
Cordray, David S. 1987. "Strengthening Causal Interpretations of Non-
Experimental Data: The Role of Meta-Analysis," unpublished manuscript to
appear irt.-L. Sechrest, J. Bunker, and E. Perrin, ed. , Improving Methods
in Non-Experimental Research (Menlo Park, Co.: Sage Publications).
Clawson, Marion. 1959. Methods of Measuring the Demand for and Value of Outdoor
Recreation. Reprint No. 10 (Washington, D. C. : Resources for the Future),
February.
Glass, G. V. 1976. "Primary, Secondary, and Meta-Analysis of Research,"
Educational Researcher. Vol. 5, No. 1, 3-8.
Hedges, Larry V. and Ingram Olkln. 1985. Statistical Methods for Meta-Analysis
(Orlando, Florida: Academic Press).
Hendry, David F. 1983. "Econometric Modeling: The 'Consumption Function' in
Retrospect," Scottish, Journal of Political Economy 30 (November): 193-220.
Retelling, Harold. Dated 1947. Letter to National Park Service in An Economic
Study of the Monetary Evaluation of Recreation in the National Parks
(U. S. Department of the Interior, National Park Service and Recreational
Planning Division, 1949).
Newey, Whitney K. and Kenneth D. West. 1987. "A Simple Positive Semi-Definite,
Heteroskedasticity and Autocorrelation Consistent Covariance Matrix,"
Econometrica 55 (May): 703-708.
Smith, V. Kerry and Yoshiaki Kaoru. 1989. "Signals versus Noise: Explaining
the Variations in Recreational Benefit Estimates," unpublished paper, North
Carolina State University, revised June.
Smith, V. Kerry. 1989. "Travel Cost Recreation Demand Methods: Theory and
Implementation," unpublished paper, North Carolina State University,
revised May.
Trice, Andrew H. and Samuel E. Wood. 1958. "Measurement of Recreation
Benefits," Land Economics 34 (February): 195-207.
Ward, Frank A. and John B. Loomis. 1986. "The Travel Cost Demand Model as an
Environmental Policy Assessment Tool: A Review of Literature," Western
Journal of Agricultural Economics 11: 164-78.
White, Halbert. 1980. "A Heteroskedasticity Consistent Covariance Matrix
Estimator and a Direct Text for Heteroskedasticity" Econometrica 48:
817-38.
-------
3. 10
U.S. Water Resources Council. 1983. "Economic and Environmental Principles and
Guidelines for Water and Related Land Resources Implementation Studies,"
(Washington, D.C.: U.S. Government Printing Office).
U.S. Department of the Interior, Office of the Secretary. 43CRF Part 11, "Natural
Resource Damage Assessments: Final Rule," Federal Register 51 (No. 1148,
August 1): 27673 - 27753.
-------
CHAPTER 4
NEARLY ALL CONSUMER SURPLUS ESTIMATES ARE BIASED
V. Kerry Smith
-------
4.1
April 4, 1989
Nearly All Consumer Surplus Estimates Are Biased
V. Kerry Smith*
I. Introduction
After eight years of a national mandate for benefit-cost analysis in the
evaluation of new major regulations, today benefit measurement is a
significant preoccupation of many resource economists. A series of recent
papers (beginning with Bockstael and Strand [1987]) have raised important
questions about how we evaluate demand models intended for benefit measurement.
While the primary focus of this work has been travel cost recreation demand
models, the issues they raise are general and equally relevant to benefit
measures derived from single equation demand models for any commodity. By
recognizing that the consumer surplus estimates are random variables, these
authors have argued for greater attention to the construction of interval
rather than point estimates, especially when these can reflect the variation in
benefit measures arising from estimation uncertainty.
Some authors have maintained that these effects should influence the
selection of a functional specification for the demand model. For example,
Adramowicz et al. [1989] concluded their simulation analysis approximating the
sampling distributions for consumer surplus estimates by suggesting that:
"...for the linear and semi-log forms price parameter estimates
close to zero create instabilities, a feature not exhibited by
the double log and linear log forms. The analyst should be
aware of this in examining his or her results. Hence, i,f two
forms are relatively similar regarding overall fit (judged via t
and F statistics), but one has a smaller variance of the
associated welfare measure, that form should be selected"
(p. 12, emphasis added).
-------
4. 2
Bockstael and Strand do not consider this issue. They focus instead on what
the analyst assumes is the source of the model's error because this source
motivates different ways of constructing consumer surplus estimates.
This papier argues that these discussions have overlooked an important
aspect of the estimation strategies used in most applied recreation demand
modeling. Estimators are selected to provide the "best" estimates of the
specified demand function without necessarily considering how these parameter
estimates would be used. Indeed, most of the consumer surplus estimates used
for policy purposes (see Smith and Kaoru [1988] and Walsh et al. [1988]) are
derived from studies that were not specifically intended to derive benefit
estimates for the recreation resources they studied. They sought to illustrate
new estimators, test hypotheses (e.g., alternative treatments of the
opportunity cost of time), or evaluate the effects of functional form. The
Adramowicz et al. conclusion suggesting that properties of the consumer surplus
estimates should be considered in selecting a final specification for estimated
recreation demand models raises a more general issue. If benefit measurement
is the objective, shouldn't we use estimators defined to enhance the
performance of our welfare estimates rather than modifying the criteria for
selecting a functional form to "adjust" for the performance of conventional,
"general purpose" estimators with some specifications for demand models?
To motivate further consideration of this question, I develop three
points. First, most conventionally estimated demand functions will yield
biased consumer surplus measures. Because of these results, the selection of a
demand specification solely on the basis of the variability in consumer surplus
estimates can be misleading. There is no assurance that tightly clustered
-------
4.3
estimates about the wrong central tendency are better than more dispersed
estimates about the true value.
Second, I derive an alternative estimator for consumer surplus per unit of
use. This new..method accepts bias in estimated consumer surplus and seeks to
minimize the mean squared error in the consumer surplus per unit of use. The
semi-log form is used to illustrate the method because it was found to cause
problems in the Adramowicz et al. study and it is the simplest to implement.
Finally, I conclude by discussing issues associated with implementing the
estimator and by presenting some evidence from an illustrative Monte Carlo
study.
II. Properties of Marshallian Consumer Surplus Estimates
Because the consumer surplus (CS) estimates derived from most popular
demand specifications are nonlinear functions of the estimated parameters, they
will be biased even if the demand specification is correct! Table 1
illustrates this point using three common specifications for travel cost demand
models. The estimated (Marshallian) consumer surplus per unit demanded is
2
reported for each form in the first column. The next two columns report the
approximate variance and bias associated with the ordinary least squares (OLS)
estimates of these demand models. A second order Taylor Series approximation
was used to develop these relationships.
Several aspects of the derivations should be noted. As the first row
indicates, the semi-log form requires the least additional assumptions for
measures of "average" consumer surplus per unit. The other two forms require
further explanation. In the case of the linear form, the sample mean was
4
assumed to be the level of use and was treated as a random variable with the
-------
4.4
TABLE 1: Approximate Properties of Consumer Surplus per Unit
Across Demand Specifications
True
Model
CS/q
Var(CS/q)
Bias (CS/q)
- a - 0P + u
1
T-
0
no finite
moments
no finite
moments
q - a - 0P + u
-2
q
Var(q) Var(0) (1+40)
~? T~
q Var(0) times
" 2ft + 1 "
20-
- a -
ub P
- 1
K2Var(0)
are:
aThe expressions for the approximate variance and bias of CS/q in the semilog case
Var (0) Var (0)
T and r respectively.
0 0
However, we know from earlier research (e.g., Bergstrom [1962], Zellner [1978]) that the
maximum likelihood estimator of CS/q will not have finite moments. Closed expressions
for the variance and bias would therefore be incorrect. This outcome reflects one of
the hazards of using approximations to characterize the properties of nonlinear
functions of random variables. This finding does not imply that mesures of the location
and scale parameters of the distributions for alternative estimtaes of CS/q could not be
derived, and thus provides motivation for the sampling results reported later in the
paper.
The definitions for the constants involved in these expressions are given as
follows:
(1-0)'
(k
1-0
- 1)
P
(1-0)
log k)
1
2
2P
(1-0)'
- 1) -
2P
(1-0)'
(k'
P 1 B 2 P
log k) + — k1''' (log k)z -
1-0
1-0
-------
4.5
log-linear form, the choke price was assumed to be a multiple (k) of the price
selected for the evaluation, and the quantity is assumed to be the predicted
quantity that would correspond to that price. As Adamowicz et al. suggest,
there are numerous possible ways of treating the upper price limit used for
this case. - .. -.
These selections imply that the variance and bias for each estimated CS/q
measure are not exactly comparable across specifications. This is not crucial
to the argument because the objective of the table is to illustrate that even
when the true specification is selected (an assumption underlying the
derivations in each row of the table), the resulting consumer surplus estimates
will be biased. The magnitude of the bias will depend on how each estimate is
computed, what is assumed about other potential sources of error, the
performance of the estimated demand models in each case, and the true values
for the underlying parameters.
The reason why the semi-log form leads to CS/q estimates with substantial
estimated variance for small values of ft is clear. They do not have finite
moments. However, to evaluate whether there .would be improvements using another
form, one must consider the bias arising when semi-log is the true demand
specification and either the linear or log-linear is adopted because of
perceived instability in the benefit estimates. This is not reported in the
table; it it the information needed to judge the merits of the Adamowicz et al.
proposal.
The table does illustrate that the strategy they propose in their
concluding remarks (cited above) is inappropriate. The perceived variability
A
in approximate expressions for the scale parameters of CS/q, such as the
approximation used for the variance, can arise simply as a result of the
-------
4. 6
magnitude of the true value for ft in this relationship for the approximation
A
for the variance of 0. Instead, we should consider how estimators of the
demand function's parameters might be designed to improve the properties of the
consumer surplus, estimates they yield.
III. An Alternative Strategy
A simple example based on a variation of an estimator originally proposed
by Theil [1971] can be used to illustrate a different strategy for benefit
estimation. Consider the minimum mean squared error (MMSE), linear estimator
of the consumer surplus. Taking the semi-log specification for the demand
function (which is both most "popular" and regarded as among the most
unstable), a straightforward derivation of this estimator is possible. In this
case, the estimated CS/q, designated now as s, is given by 1/0. The general
form for this estimator is given in equation (1). The tilda (-) is used to
distinguish this estimator for ft from the ordinary least squares estimator used
in the derivations in Table 1.
1 T
8 CTq (1)
P
where q is a T x 1 vector of observations for the
log of the quantity demanded of the service of a
recreation site for each of T individuals measured as
a deviation from the mean of log q.
If we consider only the case of models with quantity as a function of price, as
in (2), then (3) and (4) describe expected value and variance for s with the
assumption of classically well-behaved errors,
q - - ft P + u (2)
with P a T x 1 vector of travel costs
-------
4.7
E (I) - -ft [CTP] (3)
Var (s) - (72CTC (4)
2 T
where a I - E(u u )
The mean squared, error for s is defined in equation (5). After solving the
conditions for a minimum of (5), we have equation (6) as one expression for the
corresponding estimator.
MSE (I) - (- 0[CTP] - - )2 + a*CTC (5)
ft
-T- 2 -1 -T-
s - - — r (P1? + a /ft) L PXq (6)
As with the solution to Theil's original problem, the estimator is a
2
function of true values for ft and a , which are not observable. Nonetheless,
operational counterparts can be defined. For example, Farebrother [1975]
proposed that Theil's estimator could be implemented using consistent estimates
2
of ft and a in place of the true values. By an analogous argument, a
consistent estimator for s can be defined. In what follows, the OLS estimates
2
for ft and a will be used and the estimator designated as the approximate
minimum mean squared error method (AMMSE) . •••
Implementing this estimator when the focus is on a single parameter is
straightforward and requires no new estimates. Indeed, it can be calculated
for virtually all existing studies. To describe the estimator in cases
involving multiple independent variables, I use the expression for the OLS
estimator derived by partitioning the full set of independent variables into
two components with the own price in one and all other specified determinants,
including the unit vector for the intercept, in the other. Using the
expressions for a partitioned inverse of the moment matrix for the independent
-------
4.8
variables and the cross moment with the dependent variable, the OLS estimates
2
of ft are given by equation (7) and the AMMSE using OLS to estimate a and ft in
(8).
ft - (P^P)"1 PTMzq (7)
where: Z - matrix of other determinants of demand (including a
column of ones for an intercept).
q - vector of the log of quantity (not in deviation form).
T -1 T
MZ - i - z (z z) z
s
1 -T - A 2 A -1 -T
- - - -
(P MZP + " //?) P MZq
A2 2
with a - OLS estimate of a .
With some substitutions, this can be reduced to equation (9):
1 (9)
s — -
A A-
where VA - the estimated variance for ft (i.e., a (I
P
An argument similar to that of Farebrother can be used to demonstrate that the
AMMSE is consistent. However, what is likely to be more relevant for
applications is the performance of this type of estimator in small samples.
IV. An Illustrative Sampling Study
To fully describe the comparative performance of OLS versus AMMSE in small
samples would require extensive research along the lines of Kling's recent
experimental comparisons ([1988a], [1988b]) of random utility versus
conventional travel cost demand models. This is beyond the scope of this
-------
4.9
paper, so Table 2 offers instead a limited set of experiments that may suggest
some of the issues that need to be considered in improving estimates of
consumer surplus from travel cost demand models.
Four paramejierizations of each model were considered. Two were
hypothetical and imply values for s at either end of the range from most
applications. Two correspond to actual estimates for water-based recreation
sites taken from Smith and Desvousges [1986]. The key demand parameter for
each is reported in the column headings for Table 2 (the intercept was held
fixed at 2.33). Each experiment involves 500 independent replications where
OLS and AMMSE (with the OLS estimates as the starting values) are applied to
the task of estimating s using samples of 100 observations. The true models
include only the travel cost. A fixed set of 100 values for travel cost was
drawn using the absolute values of random variates drawn from a normal
distribution with a mean of 20 and standard deviation of 28. These were
invariant across replications and experiments. The error was assumed to be an
independent normal centered at zero with a standard deviation of 5.
Table 2 summarizes the results of these experiments. As Adramowicz et al.
suggested and results described as part of the discussion of Table 1 imply,
under controlled conditions the OLS estimates of the semi-log demand model
(even when it la the correct form) lead to quite variable consumer surplus
estimates. This pattern becomes more pronounced as the absolute magnitude of
the price coefficient declines and the corresponding consumer surplus per unit
increases. However, two potentially important qualifications to this pattern
seem to warrant further study.
First, the overall pattern (across the 500 replications) for the estimator
designed based on the MSE of the consumer surplus per unit is superior to OLS
-------
4. 10
TABLE 2: Small Sample Properties of OLS and AMMSE: Some Illustrative Experiments'
s - $2.00
OLS AMMSE
0 - .0473
s - $21.14
OLS AMMSE
ft - .0125
s - $80.00
OLS AMMSE
ft - .005
s - $200.00
OLS AAMSE
All Replications
Mean 2.01 _ 2.01. , 20.34 . 22.65 .
MSE 1.2x10"^ 1.2x10 6.8x10 4.7x10
n 500 500
Postive Values of
s for OLS
Mean 2.01 . 2.01 , 31.83 - 32.25 -
MSE 1.2x10 1.2x10 2.3x10 2.3x10
n 500 474
Positive Values of
s for AMMSE
Mean 2.01 . 2.01 , 30.49 . 32.32 >
MSE 1.2x10 1.2x10 1.5x10 2.3x10
n 500 473
-82.98, 8.17 -37.77 0.34
1.3x10 5.2x10 2.7x10 8.2x10
500 500
85.80 92.82 . 105.78. 103.24,
1.4x10 2.0x10 3.3x10 3.2x10
336 273
79.64 . 93.66 88.75 , 105.56.
9.4x10 2.0x10 2.3x10 3.2x10
333 267
aThe demand intercept used in these experiments was 2.33. n designates the
number of replications used in the summary statistics for each experiment.
-------
4. 11
for small values of j8, considering both the estimated MSE and the bias.
Indeed, the average OLS estimate for CS/q is negative (because of large
negative outlying estimates for s). AMMSE exhibits comparable performance to
OLS for the lowest values of s considered. It dominates OLS in terms of
estimated MSE for s .=? $21 and based on HSE and bias for larger values of s.
Second, these results are sensitive to the assumed procedure (i.e.
pretesting/estimation strategy) that any summary of the sampling results
assumes analysts would use in evaluating the models involved. It is unlikely
that positive estimates of the own price effect would be accepted in most
applied work. Because these estimates are what give rise to the outlying
negative CS/q estimates for OLS (and AMMSE), a different performance pattern
emerges if we screen estimates and assume these would be rejected. The second
and third sets of results report the summary statistics for OLS and AMMSE when
only positive estimates of CS/q are retained to approximate the sampling
distributions. As the number of replications (n) indicates, negative estimates
for CS/q become more important as the size of ft declines.
Now the OLS performance pattern is less negative (and concern over the use
of the semi-log less dramatic). OLS remains superior to AMMSE (regardless of
which is used to screen the samples) until the experiment with the largest true
value for s. Here the record is approximately comparable.
V. Implications
Frequently the applied researcher is warned that data mining, pretesting,
or equivalently the active use of judgment in the evaluation of empirical
models is to be avoided because with this practice, one violates the
assumptions of classical inference and cannot claim conventional properties for
-------
4.12
the resulting estimates. While the analytical results underlying this
admonition are certainly correct, they imply the sampling properties of the
resulting estimators will be different than those attributed to the
conventional '("pure") formulations. At a general level, this analysis has
suggested that "different" may not mean "worse" in all cases. This may be
especially true for nonlinear transformations of the estimates where judgment
can eliminate cases that are obviously inconsistent with the theory underlying
the model.
A conclusion more specific to my objective is that there seems to be a
role for developing estimators based on the economic parameter of interest.
This strategy contrasts with one that considers the overall fit of general
behavioral models or the properties of all parameters in these models. There
are conditions (and in the case of travel cost recreation demands they
correspond to a wide range of applications) in which the approximate (linear)
minimum mean squared error estimator would have superior properties to the OLS
estimate of consumer surplus per unit of use. While these results should be
carefully qualified, they do motivate consideration of different strategies for
evaluating the stochastic properties of consumer surplus estimates. These
alternative approaches should recognize how a model's estimates are to be used
and characterize the Judgments that are made before these estimates would be
accepted for policy applications.
-------
CHAPTER 4 „ „
4.13
NOTES
*University Distinguished Professor, Department of Economics and Business,
North Carolina State University. Partial support for this research was
provided by Cooperative Agreement No. CR812564 from the U. S. Environmental
Protection Agency to Vanderbilt University.
1. In February, 1981, Executive Order 12291 was issued. It required a
benefit cost analysis for all major regulations where statutes did not prohibit
use of such analyses. While there were quite disparate views as to whether
this order alone would increase the role of economic analysis in the evaluation
of environmental regulations (see essays in Smith [1984] for early
discussions), it seems now, after eight years, to have changed the way
regulations are discussed and evaluated. Benefit-cost results are a part, and
certainly not the exclusive part, of evaluations of new and existing
regulations. See U. S. Environmental Protection Agency [1987] for an interval
review of the effects of the benefit-cost mandate.
2. This is frequently the focus of benefit transfer exercises used in policy
analyses and in summary studies designed to provide valuation estimates in
anticipation of policy evaluations. The reviews by Sorg and Loomis [1982] and
Walsh et al. [1988] for the U. S Forest Service as part of implementing the
multiple use and sustained yield legislation are examples of this approach.
3. See Mood, Graybill, and Boes [1974], pp. 180-82, for examples and
discussion.
4. Bockstael and Strand [[1987] used the total consumer surplus. By adopting
this formulation, I avoid consideration of the source of the errors.
5. The derivation underlying these results does not drop the covariance terms
as Adramowicz et al. [1989] does.
6. Another approach first identified as relevant to this problem by
Bockstael et al. [1984] was developed by Zellner [1978]. It is the minimum
expected loss estimator. Zellner's loss function expresses the mean squared
error relative to the true value of the parameter. For the semilog model, it
offers a direct estimate of the cs/q as s*
I
ft J
f
It was also evaluated in the sampling experiments reported below but was found
to be inferior in all cases to the AMMSE estimator.
7. Clearly this practice must be used cautiously. It would prevent rejecting
existing theory based on contradictions. This is not what I intend to imply
here. Rather my focus is on maintained theory underlying a model that is not
subject to test in any specific application.
-------
CHAPTER 4 4.14
REFERENCES
Adamowicz, Viktor L., Jerald L. Fletcher and Theodore Graham-Tomasi. 1989.
"Functional Form and the Statistical Properties of Welfare Measures,"
American Journal of Agricultural Economics (May), in press.
Bergstrom, A.R.* 1962. "The Exact Sampling Distribution of Least Squares and
Maximum Likelihood Estimators of the Marginal Propensity to Consume,"
Econometrica 30 (July): 480-490.
Bockstael, Nancy E. and Ivar E. Strand, Jr. 1987. "The Effect of Common
Sources of Regression Error on Benefit Estimates," Land Economics 63
(February): 11-20.
Bockstael, Nancy E., W. Michael Hanemann, and Ivar E. Strand, Jr. 1984.
"Measuring the Benefits of WAter Quality Improvements Using Recreation
Demand Models," Draft Report EPA No. CR1-811043-01-0, Department of
Agricultural and Resource Economics, University of Maryland, College Park,
Maryland.
Farebrother, R. W. 1975. "The Minimum Mean Square Error Linear Estimator and
Ridge Regression," Technometries 17 (February): 127-128.
Mood, A., F. Graybill, and D. Boes. 1967. Introduction to the Theory of
Statistics. Second Edition (New York: McGraw-Hill Book Co.).
Kling, Catherine L. 1988a. "Comparing Welfare Estimates of Environmental
Quality Changes from Recreation Demand Models," Journal of Environmental
Economics and Management 15 (September): 331-340.
_. 1988b. "The Reliability of Estimates of Environmental
Benefits From Recreation Demand Models," American Journal of Agricultural
Economics 70 (November): 892-901.
Smith, V. Kerry, ed. 1984. Environmental Policy Under Reagan's Executive
Order: The Role of Benefit Cost Analysis (Chapel Hill, N. C.: University
of North Carolina Press.
Smith, V. Kerry. 1988. "Selection and Recreation Demand," American Journal of
Agricultural Economies 70 No. 1 (February): 29-36.
Smith, V. Kerry and William H. Desvousges. 1986. Measuring Water Quality
Benefits (Boston: Kluwer Nijhoff).
Smith, V. Kerry and Yoshiaki Kaoru. 1988. "Signals or Noise?: Explaining the
Variation in Recreation Benefit Estimates," unpublished paper, North
Carolina State University, November.
Theil, Henri. 1971. Principles of Econometrics (New York: John Wiley & Sons).
-------
4.15
U. S. Environmental Protection Agency. 1987. EPA's Use of Benefit-Cost
Analysis: 1981-1986 (Washington, D.C.: Office of Policy Planning and
Evaluation).
Walsh, Richard G., Donn M. Johnson, and John R. McKean. 1988. "Review of
Outdoor Recreation Economic Demand Studies with Nonmarket Benefit
Estimates, 1968-1988," Colorado State University, Fort Collins, Colorado,
Unpublished'Paper (June).
Zellner, Arnold. 1978. "Estimation of Functions of Population Means and
Regression Coefficients Including Structural Coefficients: A Minimum
Expected Loss (MELO) Approach," Journal of Econometrics 8 (October): 127-158,
-------
CHAPTER 5
DEMANDS FOR DATA AND ANALYSIS INDUCED BY
ENVIRONMENTAL POLICY
Clifford S. Russell
and
V. Kerry Smith
-------
5.1
Demands for Data and Analysis Induced by
Environmental Policy
by
Clifford S. Russell and V. Kerry Smith*
I. Introduction
Economic analysis of environmental policies is, if not uniquely, at least
unusually difficult. Resolution of these difficulties requires substantial
investment in data collection and model construction, only some of which is
directly economic. Some of the reasons for the difficulties of environmental
benefit-cost analysis are well known, appearing in intermediate and even
elementary microeconomic and policy analysis texts. Thus, even the average
economics undergraduate major can be expected to appreciate that there is a
problem finding demand functions for many services of the natural environment
because they are public goods. At more advanced levels, they will learn about
such thorny technical issues in implementing proposed solutions to this
problem. Those interested in policy learn about the conflicting maze of
environmental legislation, including problems of overlapping jurisdiction,
^Respectively, Director, Vanderbilt Institute for Public Policy Studies,
Vanderbilt University; and University Distinguished Professor of Economics,
North Carolina State University. Partial support for this research was
provided through U.S. Environmental Protection Agency Co-operative Agreement
No. CR812564. Thanks are due Ernie Berndt, Tom Tietenberg, Peter Caulkins,
Bill Desvousges, and Paul Portney for their suggestions on research related to
this paper.
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5.2
differences in burdens of proof and, most significantly, disagreements between
laws over what role, if any, economic analysis should play.
But neither the technical economic matters nor the special policy
problems, challenging though they may be, provide the principal explanation for
our assertion that the benefit-cost analysis of environmental policy may well
be uniquely difficult. Rather, that assertion is based on the central place in
such analyses of the complex relationship between policy implementation choices
on the one hand and the relevant natural systems (especially atmosphere, water
bodies, soil and resident plant communities and ground water) on the other.
To set the stage for a more careful examination of this assertion, let us
consider the nature of the system of environmental regulation and the origin of
the complications in which we are especially interested. Figure 1 combines an
overview of the linkage between policy choice and resulting benefits, with
indications of the complications arising at each stage in the linkage. In the
next three sections we shall examine in turn each of the links in the figure:
In section II, we shall describe some of the problems implied by the
way standard setting is constrained and practiced and by the
necessity of choosing an accompanying implementation plan;
In section III, we concentrate on the central role of knowledge of
natural system* interacting with choice of implementation system;
In section IV we come to some of the more obviously and traditionally
economic issues connected with valuing environmental services.
The final section of the paper brings together the analysis of sections
II-IV with a brief assessment of key emerging policy issues to produce our
version of a catalog of data-gathering strategies likely to be most relevant
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5.3
and valuable for analyzing future decisions on the allocation and management of
environmental resources.
While our approach to identifying data needs builds from specific examples
of current policy issues, the questions raised are general ones. Thus, we do
not attempt to catalog.what we consider to be the most important environmental
policy issues in 1988 and then base an evaluation of data requirements on them.
Instead we argue that the interactions between the statutes defining the
character of environmental policy and the role of natural systems for
economic agents' behavior affect the problems that would appear on any list
that might be composed. Thus, regardless of whether one believes global
warning or indoor air pollution is among the most pressing environmental
questions, economic analysts will need to incorporate what is known about a
form of these interactions in developing their analyses
II. Choosing Standards and Implementation Plans
Table 1 (adapted from EPA 1987a) summarizes the major criteria to be
considered by the Administrator of EPA in deciding on standards under a variety
of legislative mandates. Two features of this table are especially striking.
First, the criteria used to choose standards frequently focus on a subset of
the information that would be part of a full benefit-cost analysis. For
example, under the Clean Air Act the primary standards for criteria air
pollutants are to be based on human health effects but cannot include
2
compliance costs in the process of defining the standard. In contrast, under
the Clean Water Act, the definition of one type of technology-based standard,
Best Conventional Treatment (BCT), can be based on costs (in comparison with
the marginal costs of secondary treatment at municipal waste treatment
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5.4
facilities) but not on the specific benefits to be realized at individual water
bodies.
Second, the mandates involve significant areas of overlap where different
regulatory analyses are intended to influence the same types of pollutants in
the ambient environment, e.g.: primary standards for Criteria air pollutants
and New Source Performance Standards defined on the basis of the effects new
discharge sources would have on the concentrations of these pollutants.
One important implication is that economic analysis (in this case,
benefit-cost analysis) usually involves an evaluation of the net
effect of standards chosen on some basis other than economic efficiency.
Another is that standards set under one provision of one law may well overlap
in their effects with those set under another provision or law. This raises
difficulties for the definition of benefits --at least whenever marginal
benefits are non-linear -- because of the interdependence of baselines.
Other serious problems introduced by the standard setting operation can be
considered in a few specific examples. Setting an environmental standard of
either the discharge or ambient sort requires that the regulator must:
(Richmond 1983)
identify the pollutant to be regulated.
select the form of the standard (i.e., a technology to achieve an
emissions rate or an ambient concentration).
choose the concentration or discharge amount that will be the average
target.
pick the averaging time over which the target is to be met (an hour,
a day, a week, a year...).
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5.5
define the exceedance rate(s) of interest (e.g.: a weekly average
standard might be paired with a daily upper limit).
define what constitutes a violation, taking account of the
statistical error structure displayed by the monitoring equipment and
other relevant sources of uncertainty (such as measurements made
across a sample of different applications of a technology where the
standard is technology based).
Thus, evaluating the net benefits of an environmental standard is a
complicated business. Not only do we lack information on the effects of average
(or peak, as applicable) exposures to particular pollutants (or ecological
effects of average concentrations), we also should be able to evaluate
alternative patterns of allowed exceedance. In practice we are fortunate if we
have the data from which to estimate dose-response functions over any range and
averaging time.
The case of the particulate matter (PM) ambient air quality standards
permits us to see some of the troubles that can arise even within this limited
context. The benefit-cost analysis done for PM was the most expensive of those
discussed in the EPA report cited above (EPA 1987, FN 1). It seems reasonable
to assume that the quality of the analysis reflects these expenditures.
The first and largest problem in analyzing PM benefits was that the
available laboratory evidence on the health effects of airborne particulates
did not match up with the available ambient measurements. Laboratory
toxicology suggested that particles smaller than 10 microns across were
responsible for whatever health damage was observed. Since preventing health
damage was the mandated basis of the standard, the ambient standard had to be
written in terms of these small particles. Ambient measurements, with a few
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5.6
isolated exceptions, had for years been done in terms of total suspended
particulates (TSP). As a consequence, epidemiological studies aimed at finding
health effects associated with airborne particulates inevitably labored under
an imposed errors-in-variables problem.
More fundamentally, however, analyzing the total net benefits of the 10-
micron PM standard required that the relation between TSP and the distribution
of particles by size, both before and after a standard, be understood. In
addition, the analysis does not end with health because other benefits could be
identified that depended on other sizes of particulate matter. In fact, the PM
study conducted by EPA (and subcontractors) involved separate assessments of
the health benefits (including mortality and morbidity effects), the household
benefits from reduced soiling and materials damages, and the benefits to the
manufacturing sector from reduced soiling and materials damage. The first two
relied on judgmental appraisals (see MathTech [1983]) of the "best" estimates
of dose response relationships and the last two involved the development of new
models linking consumer expenditures (on commodities related to household
cleaning) and sectoral cost functions to measures of particulate
concentrations.
The importance of the institutional setting in combination with the
technical and natural systems also can be seen in the cost estimates for the
PM standard. Developing these estimates required a specification of how
states would formulate their State Implementation Plans (SIPs), the degree of
compliance with the plans, and the resulting estimated levels of particulate
emissions. Emissions then had to be translated into estimates of the ambient
concentrations of particulates. Of course, uniform ambient air quality
standards do not imply uniform levels of actual air quality, a point we return
-------
5.7
to in Section III. The changes in air quality from a specified baseline
defined spatially will depend on how the assumed SIP describes the process
(the set of discharge reductions) used to meet the standard in each air
quality control region.
To stress the analytically arbitrary nature of the institutional context,
we report an example drawn from Liroff [1986]. When states decide how to
achieve the National Ambient Air Quality Standard (NAAQS) for a pollutant, they
may have a choice among different average levels of emission reduction
depending on which mathematical model of the local atmospheric system they
choose to use to predict ambient concentrations. Table 2, based on Liroff's
Table 2.2, shows the choice facing Ohio in designing its implementation plan
for ground-level ozone. The two alternative models lead to alternative
patterns of predicted ambient concentrations, though both would show no
violation at any monitoring site. Thus, the predicted net benefits of the
ozone NAAQS in Ohio (and generally in any state) will depend on the choice of
modeling technique, not just on the average level of the standard. Of course,
it is possible that either or both models may be wrong. Neither pattern of
reductions might in fact result in meeting the NAAQS.
Let us now turn to natural system information and modeling, and the
implications of how we handle such matters for our estimates of the benefits of
environmental standards
III. Bringing in the Natural World
The evaluation of environmental policies inevitably involves economists
with the systems that make up the ambient environment. If a policy mandates a
reduction in polluted waste water discharges from industrial and publicly owned
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5.8
sources, the streams, rivers, lakes, and ponds that constitute the receiving
waters translate the discharge reduction into ambient quality improvements that
are valued by individuals. Turning this notion around, if public policy
involves mandated upper limits for concentrations of pollutants in the ambient
atmosphere, the transportation, dilution, and transformation processes at work
in that atmosphere must have a key role in determining how much discharge
reduction has to be accomplished to meet the standard.
While this seems intuitively clear, the importance of knowledge of those
processes is greater than these observations suggest. There are two reasons
for this. One is ubiquitous; the other is found to be central to some
situations and not to others. The ubiquitous influence is space, the
differential location of pollution sources and pollution receptors in the two
dimensional plane. Additional complication is introduced by the non-linearity
of most environmental processes.
Consider the role of location. In the simple situation, a policy ia
represented graphically or mathematically by a single marginal benefit (or
damage) and a single marginal cost function. These may have as arguments
either ambient pollutant concentrations or pollution discharged. The optimum
policy is defined by the usual MB-MC condition. The addition of spatial detail
merely replicates this condition at each location. That is, efficient policies
equate the marginal benefits to the marginal costs of realizing a given level
of ambient quality at each location. In conventional Pareto efficiency terms
this corresponds to equality of the relevant sum (for that location and its
residents) of the marginal rates of substitution for environmental quality (in
relation to a numeraire) to the corresponding shadow price describing the real
costs of attaining it. The natural system is implicit in the definition of the
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5.9
real marginal costs. When perfect mixing of all pollution discharges produces
uniform concentrations of pollutant everywhere in the ambient environment --as
is roughly true for some air pollutants under certain physical and
meteorological conditions -- the simple model offers a reasonably good
approximation.
But in the largest number of cases, it does not. For a mandated policy of
emission reductions, even if that policy involves equal percentage reductions
at all sources, the amount of ambient quality improvement will, in general, be
different at every point in the relevant environmental medium. If the policy
to be evaluated involves mandated ambient quality standards, the situation is
even more at odds with the simple model. Not only will the concentration in
the standard characterize only a few points in the environment after the policy
is implemented, but which points those are and by how much the quality at every
other point is better than the standard will, in general, depend on exactly how
the standard is implemented.
Both environmental quality levels and, more important, improvements in
quality attributable to a policy are different at every point in the
environment. Moreover, every point is usually characterized by different
levels of human "use.* Thus, for example, some points in the atmosphere
coincide with dense residential population, some with sparse; some coincide
\
with industrial plants, some with office buildings, some with vacant space.
Similarly, along a river some segments will have heavy recreational use (or
prospectively have such use) because of conditions of access, bank type,
current, and temperature. Other segments may be unattractive to recreationists
for reasons having nothing to do with the level of pollution at that location.
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5.10
Therefore, the estimates of benefits of proposed (or actual) environmental
management policies are intrinsically dependent on the accuracy of our
knowledge of the natural world processes, upon the detail required for the
spatial resolution and on the implementation plan assumed in the analysis.
The net benefits of a given policy, P, can be written in fairly general terms
as follows :
(1) NB (P) - BL
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5.11
discharge at every source, that defines the vector •JD1 (P) D (P)k
I 1 n J
These discharges are transformed by the functions f. (D.) into ambient
pollution (or "quality levels; and the resulting quality at each receptor
location is valued using the functions B, ( ). If, on the other hand, the
K
policy P requires an upper limit on ambient pollution at any receptor location,
call it S^, analytical implementation implies funding a vector of discharges
satisfying the requirement. This will depend on the functions f. (D.), for we
are solving a problem of the following form:
find T>i (P) such V Z f (Dt (P)) * S^.
This is different than the description in textbooks because the policy is not
defined to meet an efficiency criterion. We simply use (1) to evaluate how its
implications relate to the net benefits realized with some baseline or status
quo position. There may be no such vector. More often, since n > m, there will
be an infinite number. The benefits flowing from the choice S. will depend on
which vector D (S, ) is evaluated. This is because every such vector will, in
general, produce a different pattern of ambient quality across receptor
locations. Further, in this general formulation, there is no presumption that
quality better than the standard is valued at zero.
To illustrate what happens if we ignore the natural system, we offer one
very simple and two not-so-simple examples. First, consider a hypothetical
region with two sources of air pollution and three receptors or agreed-on
monitoring locations. The sources are, in fact, linked to the receptors by an
atmospheric system that can be characterized by a matrix of transfer
coefficients, T, as follows:
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5.12
Receptor
I II III
Source: A 2 1 0.5
B 122
Ambient quality, Q, is determined on the basis of source discharges as:
(2) Q - DT where D - (DA> Dfi)
And the benefits of discharge reductions are assumed obtainable, as damages
avoided, from a quadratic damage function.
2 8
(3) G.(Q) - Q. for each receptor i
If initial discharges are D _ - 4, D__ - 2, the base or initial quality levels
AU • BO
are:9
(A) {Qio> - (10,8,6)
with resulting damages:
III
(5) S G± - 200
i-I
-------
5.13
The effect of what we might call environmental ignorance is illustrated by
illustrated by considering three different ways of evaluating the benefits of
setting increasingly stiff ambient quality standards, S.:
(1) We know nothing about the environment (in particular, we do not know
T), so we simply work from the regional average concentration before
the standard is set and assume that the standard is the average
concentration after it is set. Let us denote this approach to
estimating benefits as method 1. designatsd B , Then:
B/-3
Q
.
- G(S.)
J
where j indexes the severity of the standard.
(2) We still know nothing about the atmospheric system (T) but
disaggregate benefits. In this formulation, benefits are calculated
only for receptors where the initial quality level is worse than the
standard. Moreover, it assumes that at every such point, after the
imposition of the standard, quality just equals the standard. This
is method 2 (B2), given by (7):
(7) B2 - 2 G(Qlo) - G(S.j)
for all i such that Q. > S..
io j
(3) We know and use T. Implementation policy is a "roll-back" rule from
base period discharges. That is, with particular standard, S., the
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5.14
roll-back rule specifies that each discharge is reduced by the
proportion R., given by:
(8) Max (Qio) - S
R. ™ .- - -1. J
Max
so that benefits are
(9) Bj - Z |G(Qlo) - G Q(R ))
where
(10) Q
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5.15
any particular nonbinding receptor is reduced, and with it the sources for the
12 3
differences between B ' B and B diminish.
The marginal benefits calculated ignoring the natural system are an
especially unreliable guide to optimal policy choice. These results are not
simply artifacts of our example. Two more realistic cases illustrate the peril
of ignorance of the natural world's systems. The first is based on the data
developed for the Baltimore, Maryland, region in the paper by McGartland, et
al. [1988], using their air quality results (for total suspended particulates)
and translating them into versions of our surrogate benefit measures. The
primary difference is that Method 3 reflects a least-cost rather than a roll-
back scheme for implementation. So we refer to it as Method 3' (see Appendix A
for data and methods). Table 4 contains a summary of the results for total and
marginal (surrogate) •benefits for each estimation approach or level of
knowledge. The marginal benefits calculated by McGartland, et al. are shown at
the bottom of the table.
Thus, in in a much more realistic example, the methods that ignore the
natural environment produce problematic estimates of marginal and total
benefits. Method 1 shows no benefits because the base case average TSP
concentration is already below all the standards considered. Method 2 produces
substantial underestimation of both marginal and total benefits. It ignores
improvements at receptors that have quality better than the standard before it
is imposed.
Modified Method 1 depends on simple reduction of the average TSP
concentration for the region for each standard level by the same percentage as
that standard represents a reduction of the baseline standard that McGartland,
et al. use in their benefit calculations, 120 micrograms per cubic meter. It
-------
5.16
produces total benefit numbers roughly similar to those obtained in Method 3',
the method reflecting best available knowledge of the environment. But this
apparent improvement does not extend to marginal benefits. The actual pattern
obtained via Method 3' shows an early peak at 110 ug/m , followed by a dip and,
then, subsequent increases. Indeed, marginal benefits are still increasing at
the strictest standard shown.
Of course, one might criticize this example as well, nothing that we are
not working with a 'real' damage function. Our last example does just: that;
using data on water quality changes, as measured by dissolved oxygen, generated
by a complex and quite realistic model of the Delaware River Estuary; a mapping
of dissolved oxygen (DO) into sustainable recreation types from a second
source; and an annual per capita willingness to pay for the availability of
water-based recreation by type from a third source. (The details of the data
and calculations are set out in Appendix A.) The results for total and
marginal benefit estimates are given in Table 5.
Thj patterns of marginal benefits once again display the largest effects
from ignorance of the natural world. Method 1 implies there would be no
benefits of going from the baseline situation to a standard of at least 3.5
parts per million (ppm) of DO for every reach of the river. But the marginal
benefit of tightening the standard from 3.5 ppm to 5.0 ppm of DO is 420.2.
L 5
Under Method 2 -- reach-by-reach disaggregation, but assuming benefits only for
reaches that are initially worse than the standard -- the marginal benefit of
the 3.5 ppm standard is 184.5 and that of the 5.0 ppm standard is 326.1. This
pattern is almost exactly the reverse of that observed when complete knowledge
is used in Method 3. In this case, the marginal benefits associated with the
lower standard are 372.7, while those associated with the next improvement to
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5.17
5.0 ppm are 208.7. Thus, even though the total benefit estimated to be
associated with the tougher standard are roughly similar for Methods 2 and 3,
the marginal benefit patterns are very different.
The results of these examples may be so obvious that their applicability
seems doubtful. Who would ever use methods such as (1) or (2)? The answer --
and this is the key to our later recommendations --is just about everyone. An
examination of the invaluable compilation of benefit estimates published by
Freeman [1982] reveals that every one of the reported air pollution benefit
1 2
studies uses a version of B or B ' with most relying on a method very like
Method 1. The water pollution benefit studies he summarizes all use a version
2
of B in which full attainment of the most ambitious standards (or ambient
quality goals) of the Clean Water Act (CWA) is assumed.
As important as pointing out the prevalence of benefit estimates based on
ignorance of natural systems is an attempt to understand why the cause also
merits consideration. In the case of water pollution control benefits, the
answer is5 generally that insufficient resources have been invested Jr. the
research needed to -reduce our ignorance. Translating the technology-based
discharge standard definitions of the CWA into actual discharges from tens of
thousands of point sources of water pollution is hard enough. But then
translating such changes in discharges, were they available, into changes in
water quality indicators that in turn can be valued by individuals involves
data gathering, modeling, and basic conceptual research efforts beyond what the
12
sponsors of such research have been willing to pay. Finally, the data on
valuation that is available generally is in the form of step functions unsuited
to the valuation of benefits of small improvements in quality, especially at
reasonably clean receptor locations.
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5.18
For air pollution benefits, the state of the art of emission inventories
and air quality modeling has for some time been capable of supporting the sort
of disaggregated, location-specific benefit estimates obtained by McGartland et
al. [1988] for Baltimore. When national total benefit estimates have been the
object of the exercise, however, it apparently has been too daunting a task to
manage the necessarily massive data banks and atmospheric models.
Finally, before we turn to the next concern of this paper, the valuation
of environmental quality changes, we should consider the effects of
implementation plans on benefits. This is the primary concern of McGartland et
al. [1988]. While their paper actually is addressed to the relevance of
benefit estimates for the choice between regulatory approaches ("command and
control" versus use of economic incentives), their results provide a fine
illustration of the point that for any given level of environmental knowledge,
estimates of benefits will depend on the method of implementation -- the
pattern of discharges -- assumed.
Thus in Table 6 we reproduce their marginal benefit estimates for the
command and control and "least cost" implementation approaches. In this case,
neither set of estimates can be characterized as "wrong." Both reflect the
best environmental information available. Nonetheless, they are very
different. Thus, the statement that a particular standard yields particular
benefits has meaning only when an implementation method is explicitly assumed.
The same standard, treated as an upper bound on a pollutant's allowable
concentrations, can imply an infinite number of aggregate marginal benefit
patterns because these benefits will depend on how the standard is implemented
and on what the natural system implies this implementation plan will yield as
the ambient concentrations for each receptor location. In most theoretical
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5.19
treatments of these issues, this problem is avoided by simplifying assumption.
The benefits are taken to be measured at a single, representative point in the
environment. The costs of improving quality at that point are assumed to
reflect the environmental transformations implicitly.
IV. Evaluation Benefits: Learning from Past Research and Identifying
New Initiatives13
The statutory guidelines creating the demand for valuation measures for
environmental resources and the time horizons written into the statutes make it
impossible to develop new benefit-cost studies for each decision. This has led
to growing interest in the methods used to transfer valuation (or demand)
estimates derived in one situation to a new one. Both the McGartland et al.
[1988] study of air quality in Baltimore and our own analysis of water quality
in the Delaware River used valuation estimates derived from one or more studies
in the literature (see Appendix A). For the most part, these were derived from
judgmental reviews of the literature and propose a best estimate (or a range of
values).
Because the services of environmental resources exchange outside markets,
the methods used to estimate consumers' values for them have developed along
two lines. The first focuses on observable behavior that can be linked by
assumptions to the resource of interest. Methods relying on this strategy have
usually been labeled the indirect approaches. They include: the travel cost
recreation demand models, hedonic price functions (property value and wage
rate), hedonic travel cost functions, damage-averting cost models, and factor
productivity (or reverse value added) methods. In each case, an individual's
(or a firm's) actions are assumed to be partially motivated by a desire to
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5.20
obtain the service of an environmental resource (or to avoid the detrimental
effects of pollution to that resource). Using models based on these actions,
researchers attempt to estimate the marginal value of changes in the quantity
or the quality of the nonmarketed resource.
The second group of methods relies on survey techniques that ask
respondents how they would value (contingent valuation) or change their
behavior (contingent behavior) in response to a postulated, hypothetical change
14
in the services of an environmental resource. This method assumes that an
individual's response to a hypothetical situation provides an authentic
description of how he (or she) would respond to an actual change.
The purpose of this section is to suggest that efforts to summarize and
evaluate benefit estimates offer another kind of opportunity --to evaluate
what we have learned about the values of environmental resources; to examine
the sensitivity of these estimates to the modeling decisions required to
develop them; and, based on these two appraisals, to identify new data and
analyses required to resolve the uncertainties leading to the disparities in
valuation estimates. The required analyses treat the results from past studies
as data to "test" whether differences in the estimates (across studies) reflect
systematic variations in the resources being valued or in the assumptions and
the methods underlying them.
While this approach appears to be a new one for evaluating empirical
research in economics, it is not new to other social and health sciences.15
"Meta analysis" describes a research method that seeks to provide systematic
summaries of the findings from empirical evaluations of educational or social
programs. Du Mouchel and Harris [1983], for example, proposed a similar
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5.21
strategy for the transfer of risk assessment models from animal to human
populations.
Our objective is broadly similar. However, we seek to evaluate whether
there are systematic influences on the values estimated for specific types of
environmental resources and whether these influences can be distinguished from
the assumptions and features of the methods. Ideally, such an analysis would
be undertaken within a single empirical study where consistency in data
sources, reporting conventions, and statistical modeling criteria could be
maintained across the resources and models studied. Unfortunately, this was
not possible. Consequently, we summarize the results of a pilot study
conducted by Smith and Kaoru [1988] that uses the existing literature as the
basis for an examination of the determinants of valuation estimates for
recreation resources. The focus on value estimates is deliberate because,
regardless of the original objective of the research, benefit estimates have
been the single most important policy use of the outputs this type of research.
Equation (1) defines the basic model. To use it, we maintain that the
valuation estimate relevant for our example, the real consumer surplus, RCS,
per unit of use of a site is a function of four types of variables: the type of
recreation site, X.; the assumptions inherent in the model specification, X^;
the form of the deaand model, X_; and the estimator vised, Xg.
(11)
where X and a., j - S, A, D, E are conformably dimensioned vectors and e^ is
the stochastic error for the ith estimate.
Smith and Kaoru [1987, 1988) have reviewed over 200 published and
unpublished travel cost demand models prepared over the period 1970 to 1986 and
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5.22
developed a data set summarizing the valuation estimates, features of the
resources involved in these demand studies, and characteristics of the models
involved. The results reported here are based on 77 studies. They yield 734
observations for the consumer surplus per unit of use. The individual
observations vary by recreation sites, demand specification, modeling
assumptions, and estimator used.
There was enormous variability in the information reported across studies.
Often the objective of the research was something other than estimating the
values for a recreational facility. It may have been testing a specific
hypothesis, with the results reported confined to the specifics of the
hypothesis test. Smith and Kaoru did not attempt to contact individual authors
to supplement (or check) what was reported in the individual papers. Rather
their data set relies exclusively on the information reported within these
limitations. Table 7 defines some of the variables that could be consistently
defined across the studies in each class of variable.
To interpret the results obtained from statistical analyses of valuation
estimates across different studies, we must formulate specific hypotheses
concerning how and in what dimensions these estimates might be sensitive to
modeling judgments. A beginning step in this process can be found in past
literature reviews (i.e., Ward and Loomis [1986], Smith and Desvousges [1986])
as well as in what seem to be established conventions in developing travel-cost
demand models. A few such protocols would include:
(1) Use trips as the quantity measure where possible, and attempt to
segment the sample when it is known that the length of stay per trip
is different.
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5.23
(2) Take account through sample segmentation of differences that might
arise from use during different seasons, or during different time
periods when there may be different time or resource constraints.
(3) Treat travel time as an element affecting the cost of a trip.
(4) Include vehicle-related costs and the costs attributed to travel time
as well as any entrance fees or site usage costs (i.e. parking costs,
lift fees for skiing, etc.) in the unit cost estimated for a trip.
(5) Use substitute prices to'measure effects of substitute sites rather
than an index of substitution; complete systems of demand functions
are unnecessary if the objective is to measure demand for one of the
sites.
(6) Reflect quality features of the site in the demand models.
(7) Recognize that heteroscedasticity is likely to be an issue with zonal
data and that selection effects can be important with individual
data.
(8) Avoid the problems posed by cost allocation issues that can aris"
with multiple destination trips by segmenting the sample according to
the distance traveled to the site.
(9) Substitute sensitivity analysis for strict adherence to one
particular functional form for the demand function.
Equally important, areas exist for which there are either insufficient
data or the absence of a clear consensus. These are:
(1) the measurement of the opportunity cost of travel time; simple
scaling of the wage rate was not found to be consistent with several
of the demand studies based on individual data, yet explicit
recognition of multiple prices for recreation time is generally
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5.24
beyond the'information set available in most current studies; no
compromise has been proposed to deal with this problem;
(2) the treatment of the attributes of a site's services;
and
(3) definition of a recreation site for modeling demand, especially where
there are many comparable sites within a small geographic area or
where there is one large "site" that extends over a wide area.
What has been missing in past assessments is some gauge of how important the
decisions might be in influencing the valuation estimates that result.
From the perspective of being able to transfer valuation estimates, we
would prefer that the empirical estimates of equation (11) be consistent with a
maintained hypothesis that o - a_ - a_ - 0. That is, judgmental modeling
assumptions contribute to the variability in benefit estimates but do not
impose systematic influences on the size of the benefits estimated. Of course,
to the extent this is not our conclusion, then we believe the process has
identified areas where further research, modeling, and data collection may be
warranted.
Table 8 provides some descriptive statistics from the Smith-Kaoru data on
the features of the studies, classified by the type of site involved. It
reports the number of estimates for each type of resource, the mean and range
in real consumer surplus (per unit of use) estimates, the proportion of the
studies based on individual (as compared with origin zone) data, and the range
of years represented in the studies. It is clear that there are exceptionally
wide variations in the consumer surplus per unit of use -- from under $1 to
over $100 in five of the seven cases. Two of these have estimates over $200.
These differences could represent dramatic differences in the character of the
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5.25
resources in each group, in the models used, or in the characteristics of the
recreationists in each sample.
Table 9 reports the ordinary least squares (OLS) estimates for five models
which consider whether the variations in real consumer surplus across studies
can be "explained" by the classes of variables hypothesized in equation (11).
Models 1 and 2 in the table contain the least variables, with 1 considering
only qualitative variables describing the type of recreation site and 2
variables describing the model specification. The remaining three models
introduce groups of variables to illustrate the sensitivity of the estimates to
the model specification, as well as to the reductions in sample size implied by
these more detailed formulations. These reductions arise from the incomplete
information available in the papers used to construct the Smith-Kaoru data
base. Model 5 is their preferred specification.
The numbers in parentheses below the estimated coefficients are the t-
ratios calculated with the OLS standard errors. Those in brackets below models
3 through 5 are the t ratios using the standard errors ».stim*,«:ed from the
Newey-West [1987] proposed adaptation of the White [1980] consistent covariance
matrix. They are reported to gauge whether the panel nature of these data
might have influenced any judgments on the importance of variables describing
the sites or Che modeling decisions.
The Smith-Kaoru data set is a panel because there are a number of cases of
multiple consumer surplus estimates reported from a single study. These can
reflect different models estimated with data for a. common recreation site,
different sites and associated data, or both. Given this diversity in the
source of multiple observations per study, the model does not readily conform
to either a simple fixed or a random effects model. Newey and West's
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5.26
covariance estimator allows for a generalized form of autocorrelation and
heteroscedasticity. As such, it provides a convenient gauge of the potential
effects of the stochastic assumptions maintained in estimating the determinants
of the real consumer surplus.
Several conclusions emerge from this statistical summary of the
literature. The results clearly support the basic approach to reviewing
empirical literature. The models' estimates indicate that the type of
resource, the modeling assumptions, specification of the demand function, and
estimator can influence the resulting real consumer surplus estimates.
For the most part, individual variables had effects consistent with a
priori expectations. Nonetheless, there is at least one important aspect of the
variable definitions that should be recognized. Our site classification
variable is not a class of mutually exclusive categories. Some sites fall in
multiple categories. For example, a state park with a lake would imply unitary
values for both of these variables. The estimated coefficients must also be
interpreted relative to an omitted category (coastal sites and wetlands),
because all sites fell within at least one of these definitions. Thus the
differential a state park with a lake would imply in per unit consumer surplus
over coastal areas is about $2.00. Nearly all the variables describing
modeling decisions were found to be statistically significant factors in
describing the variation in real consumer surplus.
Examples of these results, that are on the one hand consistent with
intuition yet also disturbing from the perspective of developing benefit
estimates that are readily transferred, include the effects of the treatment
of: substitute price measures; the value of the opportunity costs of time; the
specifications used to capture the effects of multiple sites (e.g., the
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5.27
regional travel cost model); the demand specification (notably the double-log
form); and estimator used to account for the truncation effects present with
site-intercept surveys.
Overall these findings emphasize the sources of ambiguity in demand
modeling described earlier. While the Smith-Kaoru findings are just a start
and should be interpreted cautiously, some specific areas can be targeted
despite this qualification. More careful consideration is warranted of why the
treatment of time costs and the selection of an estimator are so important to
these valuation estimates. In the first case, the sensitivity reflects the
fact that we do not know how the constraints to an individual's time affect his
recreation decisions or how an individual's implicit values on time vary with
the nature of his choices. Data can be sought on both issues.
Similarly, the importance of the choice of estimator probably reflects the
difficult subsidiary issues involved in deciding how to deal with the sampling
(Shaw [1988]) and selection (Smith [1988]) effects associated with intercept
surveys. An effort to improve the situation through data collection would
involve returning to the early population surveys (i.e. samples designed to be
representative of all households, not Just users) that elicited information on
households' recreation choices. These surveys originally were sponsored by the
Bureau of Outdoor Recreation (see Cicchetti et «1. [1969]). However, any new
surveys would require information on the sites individuals use and their
patterns of use to overcome the problems that arise in the on-site surveys. (The
early BOR surveys did not collect this type of information.) Understanding the
"market" for a recreation site lies at the heart of evaluating why substitute
prices and the qualitative variable for regional travel cost models were
important.
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5.28
We know very little of how individuals learn about and subsequently define
(for choice purposes) the recreation opportunities available to them.
Decisions on the use of "local" recreation sites versus more distant "national"
sites will most, certainly be made with different time horizons and constraints.
How are these decisions to be distinguished and can they be modeled separately?
Progress in modeling recration decisions requires answers.
The empirical models also identify an important role for the functional
form selected to describe demand. The recreational demand literature has seen
increasing criticism of the use of arbitrary specifications selected largely
for convenience or based on some fitting criteria. Several recent studies have
argued that behavioral derivations of demand models would be preferrable. That
is, they suggest models should begin with specific utility functions and derive
estimating equations by assuming optimizing behavior and by specifying the
budget and time constraints assumed to face individuals. Of course, analytical
tractability constrains how these efforts can proceed.
We believe thai, there is not an obvious answer t? the question of imposing
prior theory versus using approximations. In a genuine sense, all applications
are approximations. What is important is whether they way they are undertaken
affects the findings in important ways. The Smith-Kaoru results indicate that
greater efforts are needed in developing more robust specifications. Both
enhanced data and theory will be required to meet this need.
V. Recommendations for Data and Analytical Development
When compared with the effort and experience devoted to the conventional
topics considered under the auspices of the Conference on Income and Wealth,
the record of empirical analyses of public policies for the management of
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5.29
environmental resources is quite limited. While there has been rapid progress
in the last two decades, our ability to deliver estimates of individuals'
values for a wide array of environmental resources and, & fortiori, for changes
in specific aspects of resource quality lags significantly behind the
expectations of current environmental statutes and the projected needs for
coming to grips with emerging policy issues. We have tried to describe the
sources of these demands and the clear interaction between the needs for
economic and non- economic information,
In what follows 'we propose to use three themes to organize our proposals
for new data developments in support of empirical research in environmental
economics: learning about natural systems, learning what we know, and
responding to emerging policies. As we noted at the outset, our objective is
to consider first generic problems extending over multiple problems that
require data and second, broad classes of environmental problems that seem
likely to be important policy issues in the near future. The policy
orient:* c? on is del 'vr addressing data and modeling needs
are scare, and we need to consider their net returns here just as in other
allocation decisions.
A. Learning About Natural
As we have stressed at several points, analysis of the benefits (or
damages) of proposed or actual changes in the use of natural resources
inevitably depends on our abilities to trace the effect of the changed use
through to a change in the valuation by consumers of a resource service. This
implies that we must be able to:
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5.30
-characterize the current state of the relevant system(s);
-identify a mechanism by which the change in use affects the system;
-model how. the change has affected (for ex post damage assessment) or
will affect (for.ex ante regulatory analysis) the ambient quality of
the system in terms relevant to consumer valuation.
In many cases, our knowledge is deficient in every one of these
categories. For example, we have a lot of data on water quality but are
generally short of information that systematically covers all the water bodies
that our activities affect and that our regulations are designed to protect or
enhance. Further, the available information usually covers items relevant to
scientists' search for understanding of aquatic biological or chemical
processes rather than those that can be related to consumer valuation. Even
so, to a large extent, our abilities to model aquatic processes are inadequate.
The models often do not accept as inputs discharges or give as outputs
indicators of use or of resulting ambient quality relevant to policy evaluation
needs.
The great need here is for data gathering and model building efforts to
reflect the demands of policy analysis. Identifying the need is a great deal
easier than meeting it, for the required interaction has all the difficulties
of interdisciplinary research plus those of interstate and interagency
jurisdictional disputes. Leadership from U.S. EPA and the Council of
Environmental Quality clearly is called for.
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5.31
B. Learning What We Know
Nearly a decade ago, in closing his overview of the state of the art in
benefit estimation, Freeman [1979] observed that economists could advise the
EPA administrator how to measure benefits from a particular pollution control
policy. All that was needed were the data and learning that accompany
implementation. The intervening decade has seen some positive investments in
both data collection and in empirical modeling. However, we cannot be overly
sanguine about what has been accomplished. For the most part, the efforts have
been very specialized -- relying on existing data on consumer behavior or
developing special purpose contingent valuation surveys to estimate how
individuals would value (or respond to) changes in very specific resources.
This process has made it clear that under currently shrinking budgets (or even
with modestly expanding resources), we cannot possibly estimate the values for
all the resources of current interest.
The notion of evaluating the conditions for transferring estimates from
one resource to another is a relatively new one. Tt has been an important part
of the practice of developing the information benefit-cost evaluations
involving non-marketed resources. Freeman [1984] distinguished top-down and
bottom-up transfers, where the former attempts to allocate an aggregate benefit
for a change in *11 of one type of resource (e.g.. the share of the national
benefits from a water quality improvement attributed to one site), and the
latter refers to using micro-estimates for the household and a specific
resource in other contexts and aggregating. Naughton, Parsons and Desvousges
[1988] recently have considered the generic issues in performing benefit
transfers at the micro-level using the pulp and paper industry. Their results
suggest that a tranfer-based strategy for policy analyses is desirable but may
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5.32
require restructuring the design of future benefit estimation studies for
environmental resources.
Another possibility proposed by Mitchell and Carson [1986] involves using
survey methods to obtain estimates for national improvements in an
environmental resource from individual households. These estimates would then
be attributed to individual areas based on the amount of the resources present
in the area. The example these authors used involved water quality
improvements, and comparison of their approach with the results from a separate
contingent valuation indicated a fairly close correspondence between the
estimates derived from a specific survey and those from their national survey
adjusted with their proposed proportioning method. At this stage, however, the
literature is very preliminary. There has been no attempt to develop how the
tasks invovled in deriving transferrable models are related to the factors
(i.e., household and resource characteristics) affecting the variation in
benefit estimates across resources and user groups.
First, we a.i'2t learn wr;at we know from experiences to date, and then we
must proceed to identify what we need to learn. There is a long tradition in
resource economics involving attempts to develop consensus practices in
benefit-cost analysis and even specifying benchmark valuation estimates for
resource services most closely aligned with water resource projects. These
attempts were traditionally associated with the Water Resources Council. Our
suggestion here is that we should extend these efforts to the .valuation
estimates for all environmental resources and thereby move beyond a judgment-
based, single value for each type of resource service.
By treating the existing set of estimates for changes in the quantities or
qualities of environmental resources, it is possible to develop a systematic
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5.33
appraisal of whether the scate of the art has advanced to the point where we
can associate variations in estimates with differences in the procedures used
or with features of the resources (or consumers) involved. This process should
identify the areas with greatest uncertainty.
The experience with the Smith-Kaoru pilot study of travel cost demand
studies suggests that a more systematic approach, contacting authors to fill in
missing details, is essential if a reasonably adequate database is to be
developed in areas in which there has been less research activity. Such
efforts would also promote the development of statistical methods for dealing
with the unique features of "panel" data sets composed from existing empirical
studies.
C. Emerging Policy Needs
We have classified our views of the emerging policy needs into four
categories and consider each in turn.
1. Environmental Risk
This is one of the most difficult areas for current uses of economic
analysis, especially because it appears that individuals' responses to a wide
range of enviromental risks do not conform to our conventional
characterization of rational behavior. A recent EPA publication (see U.S.
Environmental Protection Agency [1987a]) has highlighted just how dramatically
inconsistent are public concerns and the rankings of environmental risks based
on expert opinion (U.S. EPA [1987b]). A comprehensive program of data
acquisition and research is needed to determine how and why households value
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reductions In these types of risks more highly than other sources that often
have greater likelihoods of serious effects.
This type of analysis will be important to the design of information
programs associated with pollutants EPA does not currently regulate, such as
radon, and to the development of labeling standards for products for which they
do have responsibility. It is also likely to play a central role in defining
"clean" for Superfund sites, in establishing priorities for policy initiatives
involving monitoring the underground storage tanks, and in devising new
policies associated with more stringent drinking water standards.
2. Air Quality
Acid deposition is hardly "emerging" as an issue; rather the reverse. But
that is not because the scientific questions have been answered and the
problems solved. Indeed, there is still debate in the scientific literature
over the relative contribution of different compounds and source locations to
observed low pH f»reeipitati«p fog. and dry e.r?dic deposition. Under these
circumstances, benefit estimation linked to a discharge-reduction policy cannot
proceed to meaningful results. So a clear need is for further research into
long-run atmospheric transport and chemical transformation processes, with the
ultimate aim of allowing predictions of the form: If we reduce sulfur dioxide
(SO.) discharges in this region by this much, average pH of precipitation in
this other region will increase by this much.
Even then we shall still be several steps from successful benefit
estimation for a policy of SO. reduction. It must be possible to extend
predictive natural system models to such issues as the link between average
annual (or season-specific) precipitation, pH, and soil quality to vegetation
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health and growth, and to aquatic ecological system functions. For example, if
we reduce SC>2 discharge in the Middle West, will New England and New York lakes
and ponds have better fish populations (more and larger fish of more highly
valued species)?
Only with those tools in hand will it be possible for economists to
produce meaningful benefit estimates for the sorts of policies that are
regularly debated in the Congress. To prepare for that day, the problems of
benefit (or damage) function transfer must be addressed in this problem
setting. In particular, it is necessary to consider how best to use the
results of national studies on the one hand (e.g., Vaughan and Russell [1982]
and local studies on the other (e.g., Smith and Desvousges [1986]) to value
regional effects.
A second air quality issue with even larger potential economic
implications is ground-level ozone and particularly the value of trying to
attain the currently mandated National Ambient Air Quality Standards for that
secondary pollutant. Here it is necessary to iuurove our knowledge of:
-the sources and actual levels of the precursor pollutants (especially
volatile organic compounds (VOCS)), of ground level ozone in urban and
rural areas;
-the morbidity effects of different levels of ozone;
-the effects of-ozone on vegetation and a variety of materials such as
paints, plastics, and synthetic rubbers.
Our estimates of the damages attributable to days of sickness of various types
and severities must be refined. Moreover, theoretically consistent but
practically implementable ways of measuring the value of damage to materials
providing services to households, businesses and governments must be developed.
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3. Water Quality
One of the key policy initiatives in water quality will be associated with
the national estuarine program. For point sources of waterbome pollution, the
first round of effluent guidelines will be in place with over thirty
regulations promulgated. All should be in place by the early 1990s. The
future here is best characterized as one requiring extensions in the ability of
economic valuation to realize greater degrees of resolution in valuing small
changes in pollutants.
Present methods and data would not permit such evaluations. Clearly an
improved understanding of the linkage between the technical dimensions of water
quality and individuals' perceptions of and corresponding valuations for that
quality will be necessary.
Non-point sources, especially agricultural runoff of pesticides and
fertilizers to surface waters, represent the largest unregulated source of
water pollutants. Presently, EPA lo«ss not l»*ve. •withoi.J.ty :o regulate these
sources. However, recent opportunities to coordinate the selection of areas
for the Department of Agriculture's Conservation Reserve Program, based on the
effects of pollutants on water resources, expose a new area for economic
valuation. Can we we set priorities for the selection of lands for inclusion
in this system based on their contributions to non-point source pollution? To
answer this question we need both economic and non-economic data. Agriculture
has been willing to pay premia over normal reserve payments for withholding
lands that might otherwise contribute to impairing significant environmental
resources.
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4. Stock Pollutants and Global Climate Change
This last area is fundamentally different than the first three emerging
issues we discussed in that the policy time horizon is long-term and extends
over several decades. While not a new issue (Revelle [1985] has suggested it
was identified over 100 years ago), it has achieved a more prominent role on
the policy agenda with the Global Climate Protection Act of 1987. This
legislation assigns EPA the responsibility of summarizing the scientific
understanding of the greenhouse effect (i.e. the role of the accumulation of
carbon dioxide, chlorofluorocarbons, methane, and other trace gases in the
upper atmosphere in increasing average surface temperatures on earth) and in
enumerating the policies available for stabilizing these concentrations.
As in our other examples, a key need in this area is for greater
understanding of the natural system. In this case it is the link between these
atmospheric gases and the extent and timing of any global warming, as well as
of the implications of that global warming for regional weather patterns. This
issue raises SOBS distinct methodological needs because of the extent of
scientific uncertainty over these questions, the tine horizon for the potential
climatic changes, and the irreversibility of the process.
The requirements for economic information depend, in part, on the progress
made in improving our understanding of the natural system. As this proceeds,
there is a clear need to understand the processes by which economic activities
adapt and the institutions that facilitate such adjustment. Historical and
cross-cultural analyses may well offer the only means for developing such
insights. Equally important, there is a fundamental need to describe the
inherent uncertainties in a way that is genuinely informative for policy.
While not unique to this problem, this issue of communicating the inherent
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uncertainties remains one of the most significant problems facing economists
involved in environmental policy.
Finally, in evaluating these data and modeling needs as compared with
other data priorities, it is important to recognize that in contrast to
positive uses of economic analysis where a lack of data may prevent decisions
from being made, this is not the case in normative applications. Decisions are
made regardless of whether the economic information is available. In some
cases they are very bad ones. Consequently, here new data developments
represent opportunities to improve the quality of decisions and the resource
allocations affected by them.
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Russell and Smith
CHAPTER 5
FOOTNOTES
1. To say that the analysis is difficult (and expensive) is not to say that it
is of dubious value. The U.S. Environmental Protection Agency's (EPA)
review (1987a) of its use of benefit-cost analysis concludes that for three
regulatory decisions, B-C analysis identified improvements with potential
benefits of over $10 billion (lead in automotive fuels, $6.7 bil.; Used
lubricating oil, $3.6 bil.; and pre-manufacturing review of toxic
substances, $.04 bil.). Further, EPA estimates the costs of all regulatory
impact analyses (RLAs) done under the terms of President Reagan's Executive
Order 12291 as less than $10 million. Therefore, the return to analytical
investment appears to be over 1000 to 1 in the aggregate.
Several cautions are in order in interpreting this conclusion. Most
fundamentally, our argument in this paper, if one accepts it, must
inevitably throw some doubt on these benefit estimates. Second, we canno-
necessarily project such a return ratio in the future because it is likely
that the biggest and easiest targets have already been attacked. And
finally, we should include a grain of salt because the self-interest of
those preparing the report was consistent with finding large returns.
2. This statutory requirement has not prevented benefit cost information from
being included in the Regulatory Impact Analyses prepared for cases
involving the primary standards. The proposed standard subjected to
analysis is health based. It is too early to know whether the final
standard that emerges after OHB review can be argued to have been affected
by the benefit-cost findings.
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3. Location is, of course, three dimensional, and altitude can make a big
difference in some situations; but the points we make are only reinforced
by considering a third dimension, while exposition is much simpler for two.
4. This last point is stressed by McGartland et al. [1988]. We shall return
to it below.
5. Our discussion assumes that the regulations in question will, in fact, be
complied with. Making sure this is even roughly the case requires
investment in monitoring and enforcement. These costs should be counted as
costs of the policy, and their amount and how they are used will help
determine the realized level of benefits. It is also true that choices open
in the design of implementation systems can affect monitoring and
enforcement costs and thus also indirectly affect benefits by that route.
We ignore these added complications, though they open up an entirely new
and largely unexplored source of demand for data and analysis.
6. Reasonably straightforward theoretical expositions are available that
Include differential location. For example, see F^rs-oid [19/2] and
Tietenberg [1978] and Siebert [1985].
7. The matrix T may be thought of as representing the steady-state solution to
a set of differential equations that reflects the transportation of
pollution by average winds characterized by velocities and directions, and
the diffusion of the pollution particles due to random motion in the plume.
If the units of discharge are, say (average) tons per day, the units of the
elements of T could be (average) micrograms per cubic meter.
8. For simplicity, it is assumed that the same damage relation applies at each
receptor location, though as just stressed, we would expect the damages, for
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a given pollutant concentration to differ across the various points in the
regional space.
9. Here we calculate {Q} on the basis of DQ and T, but for the argument that
follows, it. is important to note that baseline ambient quality is actually
realized and therefore can be measured. Thus, there is no inconsistency in
assuming knowledge of (Q) and ignorance of T. As a practical matter,
however, we may very well be ignorant of (Q) in any but loosest, one might
say anecdotal, sense. See, for example, Russell, et al. [1983], To be
useful, our knowledge of ambient quality conditions must be reflected in
measurements that are:
- meaningful in terms of their links with or effects on human valuation of
environmental services, and
connectable to pollution discharges that will have to be changed to change
ambient quality.
We return to this matter of baseline quality in the final section.
10. The actual pr;. terns of- orabient qunlit;.' produced by the roll-back
implementation method under the baseline and the alternative standards are:
I
II
III
Base
10
8
6
S8
8.0
6.4*
4.8*
S4
6.0
4.8
3.6a
S
u
4.0
3.2
1.6
S2
2.0
1.6
1.2
(a) indicates a quality level not reflected at all in benefit calculation (2).
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5.42
11. It should be emphasized that there Is no reason to expect a mathematically
desirable -- or even smooth -- pattern for marginal benefits. The complex
relation among standard, discharge reduction amounts and location required
under a. given implementation method, and resulting pattern of ambient quality
changes, can produce virtually any pattern of marginal benefits.
12. For a description of efforts to use natural world models in water quality
benefit estimation, although some of the threshold aspects of the B(2) method
are still used, sea Vaughan and Russell [1982],
13. This section is based on research undertaken by Yoshiaki Kaoru and the second
author and is reported in more detail in Smith and Kaoru [1988].
14. See Mitchell and Carson [forthcoming] for an overview of the issues involved
in using these methods.
15. It is not completely new to economics. Berndt's [1976] early attempt to
reconcile the diverse estimates of elasticities of substitution between
capital and labor is similar to our objectives. However, in his case, the
focus *-«-•? on thfc assumption inherent in the estimation models and Iht-.ir
likely implications for the estimates. Somewhat more closely aligned is the
Hazilla-Kopp [1986] summary of their findings on the sensitivity of the
characterization of substitution possibilities across different modeling
decisions made with the 36 different manufacturing sectors they analyzed. In
this case, the analysis parallels what we propose, but their objective was to
summarize their own findings, rather than detect sources of differences
across studies conducted by different individuals.
16. Thanks are due to Tom Tietenberg for suggesting that we make this point more
explicit based on his review of an earlier draft of this paper.
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5.43
17. Ozone is "secondary" because it is formed in the atmosphere from chemical
reactions involving sunlight and certain "primary" or discharged pollutants,
especially volatile organic compounds such as gasoline and solvents and
oxides of nitrogen.
-------
5.44
Russell and Smith
Figure 1. SCHEMATIC DESCRIPTION OF ISSUES IN USING ECONOMIC ANALYSIS
FOR ENVIRONMENTAL POLICIES
Logical Structure for Analysis
Definition of technology, discharge,
or environmental quality standard by
type of pollutant and media
Development of implementation plan
to meet standard
Change in effluent loadings
POLLUTION DISCHARGES TO THE
ENVIRONMENT
Changes in one or more dimensions of
resources depend on the spatial and
environmental resources
Change in ecological habitat and
nonhuman species
Change in human species
AMBIENT ENVIRONMENTAL QUALITY
CONDITIONS (SERVICE LEVELS)
Economic agents change their
patterns of consumption of other
related goods or their use or
valuation of environmental resources
Rationale for the Logical Structure
The institutional structure governing
the definition and implementation of
environmental policy is complex. As a
result of multiple, overlapping statutes
defined by both environmental media
(e.g.: Clean Air and Clean Water Acts)
and the types of residuals generated
(e.g.: Resource Conservation and
Recovery Act, Comprehensive
Environmental Response, Compensation and
Liability Act, etc.), policies must be
responsive to multiple objectives.
Moreover, they can involve the
definition of standards in a format
inconsistent with available
environmental data or in generic terms
that require considerable judgment to
implement, enforce, or evaluate.
The services of environmental resources
are produced within a complex physical
system. The effects of different
patterns and types of uses of these
temporal aspects of those uses. In
particular, the pattern of environmental
quality corresponding to a chosen
standard depends on the implementation
program to be used to attain the
standard.
The services of environmental resources
exchange outside markets, and therefore,
the information normally present from
market exchanges is not available.
Indeed, as part of their ordinary
consumption choices individuals may not
have been required to consider changes
comparable to those envisioned in any
specific policy analysis. Information
on the quality and character of these
services can be quite technical, involve
subtle measurement problems, and is
unlikely to be generated through the
informal processes individuals use to
learn about other commodities they
consume.
-------
5.45
Russell and Smith
TABLE 1. COMPONENTS OF ECONOMIC ANALYSIS IDENTIFIED
IN EFA'S ENABLING LEGISLATION*
Economic
Legislation/Regulation Benefits Costs Impacts
Human Other . Cost
Health Effects Welfare Compliance Effective
Clean Air Act
Primary NAAQS x x
Secondary NAAQS x
Hazardous Air Pollutants x
New Source Performance *• x * ** ** **
Motor Vehicle Emissions x x x x x x
Fuel Standards x x x x
Aircraft Emissions x x x x x
Clean Water Act
Private Treatment f *** x x x
Public Treatment f
Safe Drinking Water Act
Max. Contaminant Level
Goals x
Max. Contaminant Levels x x
Toxic Substances Act x x x . x x x
Resource Conservation
and Recovery Act x x
CERCLA (SARAi
Reportable Quantities x x
National Contingency x x
Federal Insecticide. Fungi-
cide and Rodenticide Act
Data Requirements x
Minor Uses x x x x x x
-------
5.46
Table 1. Continued
Economic
Legislation/Regulation
Atomic Energy Act
Radioactive Waste
Uranium Mill Tailings
Benefits
Costs
Impacts
Human Other
Cost
Health Effects Welfare Compliance Effective
x
x
X
X
X
x
a. Source: Adapted from EPA's Use of Benefit Cost Analysis: 1981-1986. Table
3-1, p. 3-2.
b. NAAQS designates the National Ambient Air Quality Standards and relates to
the criteria air pollutants.
c. "Other effects" refer to non-health effects on humans and firms.
d. "Welfare effects* refer to visibility and aesthetics, effects on nonhuman
species, crops, sodding, materials damage.
e. The typt .f analy.^s here ilr^rads
-------
5.47
TABLE 2. AVERAGE EMISSION REDUCTIONS OF VOLATILE
ORGANIC COMPOUNDS PREDICTED TO BE REQUIRED
TO MEET OZONE NAAQS IN SELECTED OHIO CITIES
..City '
Cleveland
Akron
Toledo
Columbus
Canton
Youngs town
Dayton
Cincinnati
Technique 1
87%
35%
47%
43%
22%
64%
61%
40%
Technique 2
50%
18%
25%
25%
10%
44%
40%
50%
Technique
Selected
1
2
2
2
2
2
2
1
a. Known as "EKMA."
b. Known as "Rollback.1
Source: Adapted from Pacific Environmental Services, Study of the 1979
State Implementation Plan Submittals (Elmhurst, IL: Report prepared for
U.S. National Commissioner on Air Quality, December 1980), pp. 7-12. and
published in Richard Liroff, 1986 Reforming Air Pollution Regulation
(Washington, DC: The Conservation Foundation).
-------
5.48
TABLE 3. AGGREGATE AND MARGINAL BENEFITS:
THE TWO SOURCE-THREE RECEPTOR EXAMPLE
Aggregate Total Aggregate Marginal
Benefits by Std. Benefits by Std.
8 6428642
B1
B2
B3
Average initial 'regional
concept of quality
relative to standard
Actual initial quality
relative to standard
Actual initial quality
0
36
72
84
92
128
144
152
168
180
188
192
0
18
36
42
28
28
30
30
20
18
18
12
relative to actual
quality as determined
for roll-back implemen-
tation
-------
5.49
TABLE 4. SURROGATE BENEFITS OF REDUCTIONS IN TOTAL SUSPENDED PARTICULATES
FOR BALTIMORE BY LEVEL OF IGNORANCE AND STANDARD (MILLION PER YEAR)
Level of
Method 1
Total
Method 1
(modified) a
Total
Marginal
Method 2
Total
Marginal
Method 3
Total
Marginal
McGartland, et al.
Marginal Benefits
(millions «f 1980
dollars)
m
0
12.3
12.3
2.6
2.6
.
7.7
7.7
7.2
no
0
23.6
11.3
6.0
3.4
19.7
12.0
12.9
105
0
34.5
10.9
9.7
3.7
27.7
8.0
9.1
Standard
100
0
45.2
10.7
15.4
5.7
34.9
7.2
8.5
(ug/m J)
21
0
55.1
9.9
21.2
5.8
46.2
11.3
13.2
1
90
0
64.5
9.4
28.2
7.0
59.1
12.9
15.1
85
0
73.6
9.1
35.2
7.0
73.7
14.6
16.4
Source: See Appendix A for a description of the data and method.
a The modification consists of comparing initial average concentration to projected
average concentrations for each standard, where the projection depended on the
percentage change in the standard.
-------
5.50
TABLE 5. SURROGATE BENEFITS OF IMPROVEMENTS IN WATER QUALITY IN THE
DELAWARE ESTUARY BY LEVEL OF IGNORANCE OF STANDARD
Water Quality Standard
" „ (ppo of dissolved oxygen)
3.5 5.0
Method 1
Total 0 420.2
Marginal 0 420.2
Method 2
local 184.5 510.6
Marginal 184.5 326.1
Method 3
Total 372.7 581.4
Marginal 372.7 208.7
-------
5.51
TABLE 6. MARGINAL BENEFITS OF REDUCTIONS IN TOTAL SUSPENDED
PARTICULATES FOR BALTIMORE BY IMPLEMENTATION METHOD AND STANDARD
(MILLIONS OF 1980 DOLLARS)
3
Level of Standard (ug/m )
Implementation
Method
Command and Control
Least Cost
115 110 105 100 95 90 85
2.2 10.5 9.7 11.5 7.5 10.0 6.5
7.2 12.9 9.0 8.5 13.2 15.1 16.4
Source: McGartland et al. [1988], Table 1.
-------
5.52
TABLE 7: DESCRIPTION OF VARIABLES FOR ANALYSIS
Name
Definition of Variables
RCS
Surtype
Recreation Site
Variable
Substitute Price
Opportunity Cost
type #1
Opportunity Cost
type #2
Harshallian consumer surplus estimated per unit of use , as
measured by each study (i.e., per day or per trip) deflated by
consumer price index (base - 1967)
Qualitative variable for measure of site use - 1 for per trip
measure, 0 for per day measure
Lake, River, Coastal area of Vetlands, Forest or Mountain
area, Developed or state park, National park with or without
wilderness significance are the designations, Variables are unity
if satisfying designation, 0 otherwise
Qualitative Variable - 1 if substitute price term was included in
the demand specification, 0 otherwise
Qualitative Variable for Measure used to estimate
opportunity cost of travel time - 1 if an average wage rate was
used
Qualitative Variable for the second type of opportunity
costs of travel time measure, - 1 income per hour used (omitted
category was predicted individual specific wage)
Fraction of wage fraction of wage rate used to estimate opportunity cost of travel
Specific Site
Demand
Specifications
Estimators Used
Qualitative Variable for use of a state or regional Travel Cost
model describing demand for a set of sites - 1, 0 otherwise
linear, log-linear and semi-log (dep) are qualitative
variables describing the specification of functional form for
demand (semi-log in logs of independent variables was the omitted
category) .
OLS, GLS, and ML-TRUNC are qualitative variables for estimators
used, omitted categories correspond to estimators with limited
representation in studies including the simultaneous equation
estimators.
-------
5.53
TABLE 8: A COMPARISON OF TRAVEL COST DEMAND RESULTS
BY TYPE OF RESOURCE
Type
of
Resource
RIVER
LAKE
FORESTS
NATIONAL
PARKS
WETLANDS
STATE
PARKS
COASTAL
AREAS
Real
Consumer Surplus
Number of
Estimates Mean
257 $17.05
483 $16.85
114 $31.36
12 $44.01
9 $45.86
107 $42.49
28 $35.49
Range
$.29
$.09
$.80
$23.48
$17.45
$.67
$.67
- $120.70
- $219.80
- $129.90
- $120.70
- $120.70
- $327.20
• $160.80
PIb YEARS0
.61 1966 - 1983
.55 1968 - 1983
.59 1968 - 1984
.50 1980 - 1983
.78 1980 - 1983
.07 1972 - 1983
.61 1972 - 1984
a. Real consumer surplus deflates the nominal estimates by the consumer price index
(base 1967)
b. This variable designates the proportion of the studies based on samples of
individual recreationists' trip-taking decisions compared with origin zone
aggregate rates of use.
c. The range of years in which the data used in these studies were collected. Thus,
this variable designates the range of years across the studies in each category in
which behavior was observed.
Source: Smith and Kaoru [1988]
-------
5.54
TABLE 9: THE DETERMINANTS OF REAL CONSUMER SURPLUS PER UNIT OF USE
Independent
Variables
Models
Intercept
23.72
(5.62)
16.07
(2.08)
20.30
(6.19)
[3.92]
27.03
(3.68)
[3.64]
18.75
(0.58)
[1.04]
Surtype
Tvoe of Site (Xg)
Lake
River
Forest
State Park
National Park
7.99 -4.13
(2.76) (-1.45)
-11.70
(-3.18)
-5.57
(-1.93)
-.45
(-0.93)
19.93
(4.44)
2.54
(0.20)
Model AfrffVttptiftll (X
Substitute Price
Opportunity Cost of
Type #1
Opportunity Cost of
Type #2
-9.97 15.38 19.88
(-2.72) (2.97) (3.74)
[-1.36] [2.34] [3.55]
-18.69 -20.32
(-3.24) (-3.52)
[-2.36] [-2.48]
-14,29 -19.03
(-2.99) (-2.19)
[-1.95] [-1.75]
-18.45 -25.99
(-2.36) (-3.01)
[-1.93] [-2.49]
24.95 22.37
(3.47) (3.44)
[3.27] [3.19]
.56 -3.77
(0.04) (-0.23)
[0.08] [-0.13]
-18.73 -13.71
(-3.27) (-2.12)
[-4.58] [-1.80]
-14.97 -16.49
(-2.10) (-2.11)
[-2.09] [-2.48]
3.95 -15.86
(1.02) (-3.30)
[0.45] [-2.87]
-------
5.55
TABLE 9 (continued)
Independent
Variables 1 2
Fraction of Wage
Specific Site/Regional
TC Model
Model Specification (JO
Linear 2.35
(0.31)
Log-Linear 14.63
(1.89)
Semi-Log (Dep) 11.26
(1.52)
Estimator (X_)
OLS
GLS
ML-Trunc
R2 .11 .03
n 722 722
Models
345
37.24 48.59
(8.56) (9.76)
[3.83] [6.94]
22.23 24.21
(4.10) (3.85)
[3.35] [2.77]
-2.87
(-0.27)
[-0.31]
23.37
(2.37)
[2.88]
16.89
(1.86)
[2.97]
-14.45
(-0.48)
[-0.84]
-8.58
(-0.28)
[-0.54]
-67.38
(-2.15)
[-3.43]
.25 .15 .42
399 399 399
a. The numbers in parentheses below the estimated parameters are the ratios
of the coefficients to their estimated standard errors. The numbers in
-------
5.56
brackets are the Newey-West [1987] variant of the White [1980] consistent
covariance estimates for the standard errors in calculating these rat-ios.
Source: Smith and Kaoru [1988]
-------
5.57
Russell and Smith
APPENDIX A
CALCULATING SURROGATE BENEFITS BASED ON THE
BALTIMORE AND DELAWARE RIVER ENVIRONMENTAL QUALITY PROJECTIONS
Air Quality Surrogate Benefits
McGartland et al. [1988] reproduce their atmospheric model's projected
patterns of total suspended particulate concentrations for 23 receptor
locations in Baltimore for two alternative implementation approaches. We used
and reproduce their Table 2 here as Table 1-A. (Ve ignore their results for 83
micrograms/m , ug/m .) We follow them in taking the pattern associated with
the 120 ug
3
/m standard as our base situation.
While McGartland et al. describe the basis for their damage, and hence
benefit estimates, they did not provide the functions they used. However, it
turns out th.'t -. surrogate function that reproduces the pattern of their
marginal benefits is easy to find. We used a simple quadratic damage
surrogate. That is:
2 3
(A-l) G. - Damage at receptor 1 - [TSP ppa] xlO
(in millions)
Benefits of increasingly strict standards are then simply:
(A-2) Bi - Gi (120) - Ct(J)
for j <120 ug/m
-------
5.58
We reproduce here, as Table 2-A, a sample calculation of the damages and
benefits for six receptor locations, one standard, and three methods.
Inspection of Table 1-A reveals immediately that Method 1 yields an estimate of
zero benefits for all standards, since the initial average quality is already
better than the strictest standard to be examined.
-------
5.59
TABLE 1-A. TSP CONCENTRATIONS BY RECEPTOR
LEAST-COST CASE
Receptor
Location
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
-120-
67.8
64.6
56.2
85.4
94.3
107.2
116.3
93.3
119.7
52.4
80.2
102.8
61.6
53.3
120.0
56.4
72.4
84.9
51.6
'7 -
64.0
64.6
105.3
-115-
67.4
63.7
56.0
83.9
92.5
102.6
113. 8b
88.7
115. 3b
51.6
78.4
101.1
60.8
52.8
114. 9b
56.4
69.9
84.0
51.4
f.5.3
63.6
64.3
102.8
-110-
66.2
62.2
55.5
81.2
89.0
99.7
107 . 8b
86.1
110. 4b
49.1
77.4
91.9
58.9
51.8
110. 4b
55.3
66.5
74.9
50.8
54.4
61.2
62.0
98.9
-105-
66.0
61.8
55.5
78.7
86.2
97. 9b
104. 3b
84.4
105. 5b
47.5
72.0
88.6
57.5
51.2
101. Ob
55.1
65.1
74.2
50.5
6.5,3
60.8
61.8
97. 7b
-100-
65.3
60.9
55.3
76.8
83.8
95. Ob
100. Ob
81.6
100. Ob
46.0
70.1
84. 3b
56.0
50.6
99. 6b
54.3
63.5
73.0
50.1
62.1
60.0
59.7
95. Ib
-95-
63.7
58.7
54.6
73.7
80.5
90. 7b
95. 5b
75.6
95. 2b
43.4
68.8
79. 7b
53.9
49.4
93. Ob
52.9
59.4
66.4
49.3
60.0
57.1
56.5
90. 4b
-90-
61.6
55.5
53.7
70.9
76. 9b
85. 7b
90. Ob
69. 9b
89. 5b
40.9
65.7
74. 5b
51.4
48.1
79. 5b
52.2
53.1
62.5
48.3
57.5
55.0
55.4
83. 8b
-85-
59.3
51.7
52.5
68. Ib
73. 5b
80. 8b
85. Ob
63. 5b
84. 7b
38.2
63.5
69. 2b
49.2
46.4
53. 3b
50.9
43.3
55.9
47.3
54.4
52.0
53.1
74. Ib
UNWEIGHTED AVERAGES OF RECEPTOR TSP LEVELS
80.1 78.3 75.3 73.3 71.4 68.2 64.4 59.6
POPULATION-WEIGHTED AVERAGES OF RECEPTOR TSP LEVELS
77.4 75.7 72.9 70.9 69.0 66.2 62.9 59.3
b Indicates a concentration reflected in the calculation of benefits using Method
2.
Source: McGartland, et al. 1988
-------
5.60
TABLE 2-A, EXAMPLES OF SURROGATE DAMAGE AND BENEFIT CALCULATIONS BY METHOD
Damages at
Receptor Base Level •"
2 4.2
7 13.5
10 2.7
12 10.6
15 U.4
18 7.2
For average level
6.4
Total
Marginal
Method 1 (modified) Method 2 Method 3
Damages Damages Damages
at 110 Benefits at 110 Benefits at 110 Benefits
4.2 0 3.9
12.1 1.4 11.6
2.7 0 2.4
10.6 0 8.4
12.1 2.3 12.1
7.2 0 5.6
5.4 1.03
x 23
23.6 6.0
11.4 3.4
0.3
1.9
0.3
2.2
2.3
1.6
19.7
12.0
For Modified Method 1, base average surrogate damages - damages at t;;
-------
5.61
Water Quality Benefits
Water quality benefits are based on predicted water quality improvements in
the Delaware estuary published in Spofford et al. [1976], The quality indicator
used is dissolved oxygen (DO) and the base levels are interpolated from their
Figure 2 reproduced here as Figure 1-A. Improvements associated with alternative
standards are taken from Table C-3 in the source. Their run using a 3.0 ppm
standard is used here as a surrogate for a 3.5 ppm standard because in all but
one reach better than 3.5 ppm is attained under it. The predicted levels of DO
for that standard and for a fun with a 5.0 ppm standard are set out in Table 3-A.
The implementation plan implicit in these runs is the least cost arrangement of
discharge reductions.
To calculate benefits, dissolved oxygen is translated into sustainable
recreation activities using the table of equivalents developed by Vaughan [1981]
and displayed here schematically as Figure 2-A. Then the three alternative
methods of benefit C3l.-cu3 it*.c*? '•••r* applied as summarized Irr Table ''-A, where the
per capita per day values of the alternative sustainable activity measures of
quality are drawn from (Smith and Desvousges [1986]).
What we have not done is to associate numbers of people with particular
receptor locations along the river. ("Receptor location" is usually called
"reach" in the water pollution field. It means a stretchof river within which
ambient quality is assumed the same.) This is difficult to do in any case
without a study to measure the recreational suitability as determined by non-
water quality characteristics. But it is even more difficult to dp within a
massive urbanized agglomeration such as that from Wilmington, Delaware, to
Trenton, New Jersey, that surrounds the Delaware Estuary. The figures in Table 5
-------
5.62
are therefore simply the sums of the relevant per capita benefits over all the
reaches. These figures exaggerate the penalty for ignorance of the environment
to the extent that more individuals could easily travel to and recreate on the
middle reaches. These are the most heavily polluted, and therefore benefits
associated with their cleanup show up in Methods 1 and 2, while any benefits
associated with further cleanup of the most upstream and most downstream reaches
tend to be ignored in those methods.
Note that the use of Vaughan's equivalence in essence begs an important
question: Do we have an environmental quality indicator that is connectable both
to discharges and to valued human uses of the environment? Dissolved oxygen is
only one of the elements of & vector of water quality characteristics that
determine how a body of water can be used. It may be the key element for fish
populations but is certainly much less important in determining whether water is
"beatable" (that is to say, pleasant to boat on) or swimmable (where bacterial
counts are turbidity are much more important).
-------
5.63
TABLE 3-A. BASE CASE AND PREDICTED LEVELS OF DISSOLVED OXYGEN:
TWO ALTERNATIVE STANDARDS APPLIED TO THE DELAWARE ESTUARY (PPM)
Reach
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
Average
Base
Situation
8.3
7.0
5.6
4.9
4.6
4.4
3.8
2.7
1.8
1.3
1.2
1.2
1.3
1.5
1.8
2.3
2.8
3.5
4.2
5.0
5.8
6.6
3.7 Standard
3 . 5 ppm
Standard
8.6
7.7
6.6
6.0
5.7
5.9
5.9
5.8
6.1
5.3
3.6
3.7
3.6
4.0
4.5
5.2
3.0a
3.7
4.8
5.8
6.2
6.6
3.5 .Standard
5.0 ppm
Standard
8.6
7.7
6.9
6.3
5.9
6.0
5.9
5.9
6.4
6.8
5.3
6.1
5.7
5.7
6.1
6.4
5.0
5.1
5.7
6.1
6.2
6.6
5.0
Source: V. 0. Spofford, Jr., C. S. Russell, and R. A. Kelley, 1976,
Environmental Quality Management: An Application to the Lover Delaware Valley
(Washington, DC: Resources for the Future).
The standard actually imposed by Vaughan et al. was 3.0 ppm. But 3.5 is a
lower bound for boatable quality qwater in the Vaughan scale, so we treat
this run as though the standard were 3.5 for purposes of Method 2
calculations.
-------
5.63
TABLE 3-A. BASE CASE AND PREDICTED LEVELS OF DISSOLVED OXYGEN:
TWO ALTERNATIVE STANDARDS APPLIED TO THE DELAWARE ESTUARY (PPM)
Reach
Base
Situation
3.5 ppm
Standard
5.0 ppm
S tandard
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
2i
22
Average
8.3 8.6
7.0 7.7
5.6 6.6
4.9 6.0
4.6 5.7
4.4 5.9
3.8 5.9
2.7 5.8
1.8 6.1
1.3 5.3
1.2 3.6
1.2 3.7
1.3 3.6
1.5 4.0
1.8 4.5
2.3 5.2
2.8 3.0*
3.5 3.7
4.2 4.8
5.0 5.8
5.8 6.2
6.6 6.6
3.7 Standard 3.5
8.6
7.7
6.9
6.3
5.9
6.0
5.9
5.9
6.4
6.8
5.3
6.1
5.7
5.7
6.1
6.4
5.0
5.1
5.7
6.1
6.2
6.6
.Standard 5.0
Source: W. 0. Spofford, Jr., C. S. Russell, and R. A. Kelley, 1976,
Environmental Quality Management: An Application to the Lower Delaware Vallev
(Washington, DC: Resources for the Future).
The standard actually imposed by Vaughan et al. was 3.0 ppm. But 3.5 is a
lower bound for boatable quality qwater in the Vaughan scale, so we treat
this run as though the standard were 3.5 for purposes of Method 2
calculations.
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5.64
TABLE 4-A. CALCULATING SURROGATE BENEFITS FOR DISSOLVED OXYGEN
IMPROVEMENTS IN THE DELAWARE ESTUARY BY METHOD
Method 1
Base Case Average: 3.7 ppm (B)
3.5 ppm Standard 3.5 ppm (B) Benefit - 0 x 22 - 0
5.0 ppm Standard 5.0 ppm (G) Benefit - $19.1 x 22 - 420.6
Methods 2
and 3
Marginal Benefits
Method 2
Base Case
Reach Sustainable Use 3.5 Standard
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
Totals
S
S
G
B
B
B
B
U
U
U
U
TJ
U
U
U
U
U
B
B
G
G
S
-
.
.
-
.
-
B (20.5)
B (20.5)
B (20.5)
B (20.5)
B (20.5)
B (20.5)
B (20.5)
B (20.5)
B (20.5)
U
.
-
-
.
-
184.5
5.0 Standard
-
-
G (19.1)
G (19.1)
G (19.1)
G (19.1)
G (19.1)
G (19.1)
G (19.1)
G (19.1)
G (19.1)
G (19.1)
G (19.1)
G (19.1)
G (19.1)
G (39.6)
G (19.1)
G (19.1)
-
-
-
326.1
Marginal Benefits
Method 3
3 . 5 Standard
-
S (35.4)
G (19.1)
G (19.1)
G (19.1)
G (19.1)
G (39.6)
G (39.6)
G (39.6)
B (20.5)
B (20.5)
B (20.5)
B (20.5)
B (20.5)
G (39.6)
U
-
-
•
-
•
372.7
5.0 Standard
-
-
.
-
.
-
'
-
S (35.4)
G (19.1)
" f!9.1>
u (ly.r,
G (19.1)
G (19.1)
.
G (39.6)
G (19.1)
G (19.1)
*
-
•
208.7
A dash (-) indicates no improvement in sustainable recreational use over the
next lower standard or over the base case as appropriate.
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5.65
Figure 2-A
DO
ppm
7.0
6.5
6.0
5.5
5.0
4.5
4.0
3.5
Sustainable Associated Annual Marginal ,
Activity Shorthand Willingness to pay per person
Swimmable S $35.4
(plus fishing
and boating)
Game Fishable G $19.1
(plus boating)
Beatable B $20.5
Unacceptable U 0
for boating
a Source: William J. Vaughan, 1981, "The Water Quality Ladder," Appendix II In Robert C.
Mitchell and R. T. Carson. An Experiment in Determlnlne Willineness to Pav for National
Water Dual
itv Improvements (Washington, DC: Resources for the Future, draft report).
Source: Smith and Desvousges [1986].
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5.66
Russell and Smith
CHAPTER 5
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