May 1, 1980 - SYSTEMS METHODS IN NSrUaAL RESOURCE ECONOMICS. Gordon C. ... These formulations of natural resource problems in a control theory framework are of ...... Churchman, C. W., The Systems Approach, New York: The Delacorte ... A Manual for âProgram RECSYSâ, Recreation Resource. Planning ...
Department of Agricultural and Resource Economics, UCB UC Berkeley
Title: Systems methods in natural resource economics Author: Rausser, Gordon C., University of California, Berkeley and Giannini Foundation Johnson, Stanley R., University of California, Berkeley Willis, Cleve E., University of Califorina, Berkeley Publication Date: 05-01-1980 Publication Info: Department of Agricultural and Resource Economics, UCB, UC Berkeley Permalink: http://escholarship.org/uc/item/0cq8950r Keywords: control theory, economic aspects, natural resources
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H
Hq Division of Agricultural Sciences I)NTVPSITY OF CPLIFORNIA
LUniversity of California, Berkeley. Dept. of agricultural and resource 1 economiCS_ orking Paper k Working Paper No. 119
S(5TEMS METhODS IN NATUIAL RESOURCE ECO1’flCS
Gordon C. Rausser, Stanley R. Johnson, and CleveWillis
GIANN1NI FOUNDATION OF AGRICULTURAL ECONQMIC
ERA F?Y 4fl
3
California Agricultural Experiment Station Giannini Foundation of Agricultural ECOrQmjL May 1980
• $ SYSTEMS METHODS IN NSrUaAL RESOURCE ECONOMICS Gordon C.
Rausser,
S. R. Johnson and Cleve E. Willis 1.
TNrRODUTION
Concern about the eftvironment and the supplies of extractive resources available from it is not a recent phenomenon.
Indeed, the study of natural.
11 resources has a rich tradition in the field of economics.
Maithus [17933
and Ricardo [1817), for example, sketched a dismal picture in which popula tion and economic growth would continue until population was checked by increasing misery, given fixed quantities of land suitable for the production of food.
This early “limits to growth” concern was extended to mineral re
sources by Jevoñs (1865], who worried about the quantity of known coal dcposits in England over one hundred years ago.
Mill’s [18631 emphasis on
qualit)- of life aspects derivable from the environment was a logical out growth of these carly concerns about extractive uses of the environment. Several decades ago, Ciriacy-Wantrup [1952) distinguishcd between re r.ewab)c and non-renewable extractive resources on the basis of existence or economically significant rates of regeneration.
The more recent literature
has developed, in a more formalized context, theories for uptiSa2 exploita tion of nattiral resources, enphasizing the difficult problems of irtertcmpG nil production atd technology; measures of benefits, utility functionals and appropriate rates of time discount; and problems presented by common prop èrty and ehternalities of production and cons’nnption.
More nadorn tudels
incorporate the urcertainty 2ssoct’tvd v’ith asc of rcnewah.e rd on-enewa’t a;iJ povin:it a
taifti9j abozit
t:o t!rnGlcay r
;:4cfl;A.L
c:,.I
the hcr•cfits fucrtion ‘m hich the time alaocatft:’ pro:eçs is bar:3 (Paser,
1t
“P
-2S
Willis and Prick [1972], Rausser and Howitt [19751).
Much of this work es
tablishes the relationship between the natural resource problem and the problem of stochastic control (Tse [1975], Athans [19721, Joseph and Tou [1961]). These formulations of natural resource problems in a control theory framework are of interest in at least two respects.
First, they emphasize
the complexity of the natural resource exploitation and allocation problems as presently perceived.
At the core of this movement to more flexible models
is an enlarged view of the concept of a natural resource. •
From emphasis on
land, extractable minerals and timber, the subjects for n4tural resource studies have expanded to include air, .the environment, wilderness, bodies •
of water, quality of life, and other resources.. These diverse and changing topics of interest for study suggest extreme care in defining natural re source economics.
Obviously it concerns problems of exploitation, alloca
tion, production and distribution of natural resources.
But perceptions of
what constitutes a natural resource have changed or at least expanded. •
In general, natural resources are often regarded as primary factors (Gaffney [1967], Krutilla [19671, Smith [1968]).
Nevertheless, it seems
clear that the concern for natural resources is very much a function of the point in time at which the related system is studied.
Resources are not
merely physical substances, but rather are products and manifestations of a continuing interaction between man and nature (Zimmermann [1951]).
The sys
tems describing both the behavior of man and relations existing in nature, and their interactions, clearly fall within purview of resource economics. Recognition of this fundamental aspect of resource economics serves to
4
-
3-.
establish its connection with systems concepts and the analytical constructs developed for their study. The second feature of interest in examining modern models for studying
natural resources relates to their technical or engineering aspects.
All
include as basic inputs detailed structures describing biological and phys— ical processes.
The appropriate framework for developing these structures
traditionally has been that of a system (Clawson [1968], Herfindahi and Kneese [1974], Nordhaus [19731).
This is particularly evident in the applied
work on resource problems. The use of systems concepts can be explicitly found in the River Basin Studies of Halter and Miller [19661, Hufschmidt and Fiering [1966] and Hamilton, e ci.
[1969].
In a number of respects these
studies have drawn on the systems framework, specialized for resource prob-. lems by Maass, et ci.
[1962] and Dorfman [1965]
.
It should also be noted
that this approach, although with a somewhat different terminology, was present in the eariy applied work on development of natural resources (Huf schmidt [1963]).
Thus, from the appropriate framewor. for defining re
sources to that for developing physical and biological structures for use in applied work, systems concepts have occupied an important role. The irpose of this paper is to docunent the importance of systems con cepts in the analysis of resource economics problems.
It will show that the
modern work extending systems concepts to economic dimensions of natural re source problems has involved so;n expense in the sense that it extends be yond the range of available general economic theory.
For this reason, re
sults of the aszociatcd application.; anat often he viewed as highly special— i zed to th problems at hand and the pcrsuns developing the models.
The
discussion concludes by suggestinç a solution to the dileoma presented by
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the apparent suitability of the source probl’rns
in
Sy’Stcrns
framework for studying natural re
economics.
In order to provide an overview of the use of systems concepts in nat ural resource economics, and to offer suggestions of future directions, it is useful to provide definitional fratne:orks for both systems concepts and natural resource economics.
In particular, since there is dazzling varia
tion in definitions of concepts in the literature on systems methods, we
define in Section 2 the systems concepts as they will be used in the succeed ing discussion.
Moreover, it should be useful, particularly to non-economists
to present a brief discussion on why natural resource economics is different from other branches of economics; to identify those dimensions which distin guish it from the topics of the other papers in this issue. is developed in Section 3.
This treatment
Selected, illustrative applications of systems
methods in the economics of natural resources are provided in Section 4 and the final section, 5, provides an appraisal and assessment of future direc tions for modeling efforts and policy analysis for natL:ral resources.
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2
-
SYSTEMS METHODS • STRATEC IFS FOP. MODEL DFVE LOPMEF AND APPLICATIONS
respects. Natural resource systems and models are special in a number of ance of considering The basic features of these systems emphasize the import methods. particular types of model construction and operational
First,
ically dy problems of optimal utilization of natural resources are intrins
namic.
nal. Current actions have delayed impacts on the objective functio
ting simpli Moreover, they are sufficiently complex that assumptions facilita fying decompositions are often restrictive.
Planning horizons are lor:g com
a comparatively pared to those for most economic models, and there is often system and ini substantial degree of uncertainty about the structure of the tial conditions (stocks) in the current time period.
Finally, the models
ic systems. typically require the merging of physical, biological and econom natural resources The result is that for most purposes, the models of such ely integrated into systems evolve through time whether actively or passiv
the optimization process. pment is difFicult As Mar [1973] suggests, a discussion of model develo ciature used ro due largely to the diverse and inconsistent sets of nomen
various disciplines. describe models, their characteristics, and uses in the view models as subrou Cited examples include Shubik and Brewer [1972), who simulation a tyoe of tines used in simulations; Raser [1969), who considers
tion as the ma model; and Meier, Newell arid Pazer [1269), who regard s5niuia nipulation of models.
This section presents a cursory review of the basic
ard application pro— systems concepts, model types, and model construction act of ncmoncIture. ceaes, with the purpose of tahi .shind a cons stcnt
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2.1
Mhc and Modc CoLLton.
In the construction and use
of quantitative economic systems models, activities which must be accom plished may be identified as analysis, synthesis, and design.
Systems
analysis is largely a descriptive stage of the model construction process; it is a process by which an investigator with a specific problem and objec tives in mind initiates the modeling and/or research process.
The system
in question is observed and the investigator’s perceptions of the problem under investigation is sharpened.
Generally, this process is one in which
the elements or components of the system are identified; the current and al ternative institutional frameworks are isolated; the principal decisionmakers are specified along with their decision variables, performance cri teria measures, and the relationship between the decision variables and performance measures.
The size and scope of the model,the level of ab
straction appropriate for the question under study, and sources of informa tion and data must be determined in the system’s analysis phase.
Finally,
is the decision—maker or decision group’s criterion ‘unction of all the relevant performance measures explicit or implicit? Systems synthesis activities involve identifying and classifying the components as to function; S;)eClfyiflg the environmental considerations; dis tilling the behavioral hypotheses; and determining the quantitative rela tionships between and within components of the system.
This is the juncture
at which the investigator’s perception of the system in terms of modeling objectives must be formalized.
In essence, it is the process which provides
the model with a cohesive structure. In the systems design stage, we gDnerally find research objcctives and elements of the model structured in such a way as to allow analysis of
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alternative policy strategies.
however, depending upon the objectives of
the analysis, the design may be simply an hypothesis as to the working of the system, the structure of a decision model or a particular forecasting mechanism.
In this regard, it is important to distinguish between the more
utilitarian design problems within the model (strategic or tactical questions) and those which involve maintained hypotheses as to the function of the sys 5/ tern (institutional questions).—
In essence, tnis process involves select—
ing the framework within which market, regulatory, structural, and institu— tional changes of systems are to be examined.
Alternatively, design may be
viewed as a process of choosing a format for combining the synthesized sys tem components and relationships to satisfy modeling objectives.
In any
event, design determines the institutional framework, which in turn constrains the sorts of strategic or policy evaluations performed with the model repre sentation.
From an operational standpoint, design issues become particularly
crucial in the use and construction of decision support systems based upon formal models. The actual construction of the model can be viewed in terms of five essential steps.
These steps are model specification, estimation, verifica
tion, validation, and revision.
Specification generally occurs after the
system has been analyzed and is one of the activities of systems synthesis. Structures deduced upon accepted normative propositions and established technical relationships have greater generality, given that the paradigm governing the modeling process is appropriate.
Models of tnis type are more
easily tested and are usually tess complex structurally.
Alternatively,
there are highi y suecial i zed models of the type encuunte ed in natural source economics based Li rgciy on I ccc :e ine! propos I ii oas
.
re
The process i s
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one of observing the system and formulating (in abstract form) the behav ioral and other structural relations.
A difficulty with these more special
ized models is that they can become highly personalized. For quantitative models, specification in\rolves a mathematical struc ture and an operating model.
In the case of natural resource models, the
relevant equations include behavioral, identity, and technical relationships. The behavioral equations attempt to represent the response of participants (represented by endogenous variables) within the system to economic and other signals (explanatory variables).
The identity or technical equations imply
exact relationships determined largely by engineering or physical phenomena. Once the model has been specified, parameters sununarizing the effects of certain variables on others must be estimated. mated using a number of methods.
Parameters may be esti
Generally, systems models either rely
heavily upon statistical methods, or reject the data because (i) it is in appropriate (Forrester [1961, 1968]);
(ii) it involves substantial error
(due to the sampling process generating the data); or (iii) of suspected structural change.
Because of the diversity of possible estimation methods
both in terms of information sources and iterative procedures involved (Wal lace and Asher [1962]), a rather general framework is needed for viewing the process of estimation.
Appropriate approaches include Bayesian (Zeilner
[1971] and Zeliner and Chetty [1965)) or Mixed Estimation methods (Aitchi— son and Silvey [1958], Judge and Yancey [1969] and Theil
[19701).
In both
instances, sample data and extraneous information on parameter distributions are systematically combined to obtain estimates of the structure. advances in Mixed and Bayesn estima en techniques also structures with nen-stio9ar:’ parameters L1dor
DiTnit
Kopeii
Rocent
CVCiV1fl
[1971], Freehi:n
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and Rausser [19761).
These data and non-data oriented estimation processes
are essentially the same, with the difference a matter of the relative cer tainty with which the extraneous estimates of the parameters are held. In addition to their appeal for the data source problem, the Bayesian and Mixed Estimation approaches arc sufficiently general to provide for the incorporation of interative procedures frequently used in choosing among model specifications (Rausser and Johnson [1975]).
In the context of these
difficulties, the Bayesian approach has been argued to be the more viable al ternative for selecting among model specifications (LThrymes, et a.
[1972]).
Learner [19701 has explored the implications of alternative weighting func tions in this context and Zeliner [1971, pp. 306-3171 has provided a general outline of Bayesian procedures for comparing and choosing among models.
A
useful summary and comparison of Bayesian and Classical procedures for dis criminating among alternative specifications of single equation models,
which reveals some promising developments, has been presented by Claver and Giesel
[1972]
Lastly, parameter estimation is aiso influenced if models are adaptive. Many times systems models are constructed, estimated and simulated and while le this process is evolving, additional data on the structure become availab (indeed, may be actively sought). context are contained in Aoki [1971]
Results which may be of value in this
[1975], Chow [19751, Prescott
[1972], Zellner
Rausser and Freebairn [l974a1, and Tse [1974]
whether Verification is the process by which the investigator determines or not the model performs in accordance with the intendcd purpose.
For ex
ample, in al gebriac models veeif cs 5 on is concerned with completeness ex istecc of solut ions, inte flOl funct on lag and so furth.
The mast cc maca
.:.
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use of the term, however, appears in conjunction with digital computer models and/or analogs.
Used in this connection the term relates to establishment
of desired isomorphic relationships between system, model, and digital analog.. The process of corroborating the model with the system is called vali dation.
This is clearly a judgmental process.
First, if the requirement is
a close corroboration with the system, how should data on the functioning of the system be summarized and compared to outputs of the model for tests of consistency?
Secondly, how important is prior information relative to the
data on the system and how should these two types of information be combined in corroborating the model?
Third, at a more philosophical level, what frame-’
work should be employed to determine which hypotheses on the system are to be tested and which are maintained? The four preceding steps may be ‘final or ‘provisional.
In a provisional
process the ‘fifth or revision step is concerned’ with an assessment as to whether or not the màdel should be altered to make it more suitable for the intended objectives.
Whatever the revisions, it is important to systemati
caliy specify the sources of information and the nethod for using the infor mation to change the model.
It is unfortunately not often recognized that
such conditions are as much a part of the prior information used to construct the model as the more frequently discussed theoretical underpinnings and data sources. Perhaps the stngle most important aspect of the modeling process is that it is an iterative one.
If the model does not forecast the behavior of a
particular variable reartonably well, or if the model does not provide the type of answers needed given the policy questions posed, then the construction should rcturn to :n earlier stage cither to improve the model spccificatin
_i 1-
To be sure,
or to suggest that other types of policy quest ions be asked.
each of these phases is reversible; ie., thu research investigator can, for example, complete phases one and two and move hack to a revision of phase one before going on to phase three.
Nevertheless, it is important to recog
riize the opportunity cost in terms of inefficient strategies with respect to unstructured movements from one phase to another.
The cumulative implications of the above observations on the model con struction process suggest that from a research strategy standpoint it is im Researchers
portant to explicitly recognize the entire modeling process.
begin with concepts from theory, results of other applied work, perhaps per sonal views and historical data on the system to develop a provisional speci
fication.
Given constraints which exist with respect to resources available
for the research project, the time frame within which the research is planned,
etc., the analyst proceeds from one previsional spccificatioo to another until a version of the modal is available which, given the constraints, sat isfies the objectives of the research endeavor.
The objectives of the re
search projects are usually stated rather clearly, and research expense allo cations, time and other constraints are also known with a fair degree of cer tainty. By recognizing the process of proceeding from one provisional structure to another as a transition between states in the implicit control problem and making more explicit the policy or strategy governing the evolution to the final vers ion of the model, research involving natural resource systems
models can law olaced en a soande r scL’t tific footing. such inferaat or on node
implicit cant un I
cons tru r
ttr;r
Tne availability of
n teroal
1
:a ;on of Lne
roblem provides a fi vu hvc is for crit i cal nopra isal of the
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resulting formulation and at the same time establishes the foundation for a more systematic process of knowledge accumulation. The entire model-building procedure is represented in Figure 1.
As rep
resented here, systems analysis is composed of isolating (i) the problem to be solved; makers;
(ii) alternative institutional frameworks;
(iii) the decision-
(iv) the decision or policy variables; (v) the performance measures;
(vi) the system’s components and relationships, and (vii) the nature of the criterion function.
System’s synthesis is largely concerned with model con
struction activities while system’s design is concerned with the actual use of the model as a decision-making aid on a timely and interactive basis. Finally, note the iterative nature of the modeling process. 2.2
Moa’e Repta;vcn.
The above steps in model construction are heav
ily conditioned upon the objectives or purposes for which model representa tions are developed.
Clearly, models can be developed for a number of pur
poses, some of which do not necessarily correspond to the purposeful func tioning of the system under examination.
Depending upon research objectives,
the investigator may use descriptive, explanatory, or predictive models. Most descriptive models are exploratory in nature.
The researcher ob
serves a system and constructs a model designed to describe the functioning of the system.
That is, “a descriptive model simply sets forth a set of
relationships which have ‘bound together’ different variables in situations in which they have been previously 1 observed (Strotz and i.old [1960, pp. 417’ 4131.
Information developed from the model is used to understand the work
ings of the system and support inferences under alternative assumptions as to conditt oidng by the environmental factors.
Descriptive models have been
—13Figure 1 Modeling Process for Decsion-Making Purposes
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1SH,\ iD
‘1)
1
ALTERNAIIVL ANU (:URRLNT INST ITUTI ONAI, Si:i T INC
RL lu nici Si ON—M\LRS’’ id io \1
-
ARE TIlE [ThCI S ION OR POLICY VARIABlES EXPLICiT
SYSTEMS ANALYS IS
>
ARE TIlE PERFORMANCE MEASURES EXPLICIT?
—>
ISillE CEll l [ON O OS CTI ‘. ii FIJNCTIO\ EXPLICIT OR IMPLIC[?
I
1 [_ MODEl. S[CIHCfOi2jj___J
1-
> S Y ST E1S SYNThESIS
L
DATA USE AND MODEl. EST EMA IflN
j
iOl)Ll. \1iIi:i(::
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MOBIl. \\LIDAI ioN
if
‘if MC)DrI.
S YST1:M3 DESIGN
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5
Mu EL USE
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-44—
rather widely employed in studies of natural resource systems; a phenomenon in part attributable to the behavioral bent of the social sciences.
Among
those who have advanced and developed descriptive modeling techniques are Forrester [19711 and Meadows, Randers and Bhrens [1972] Explanatory models are constructed with objectives similar to those for the descriptive case.
The principal distinction is that explanatory
models are causal in nature; where causality is defined in the Strotz and Wold [1960] sense.
That is, in the statistical sense, “Z is a cause of Y
if, by hypothesis, it is or ‘would be’ possible by controlling Z indirectly to control Y, at least stochastically”.
Relationships specified in these
models involve assumptions as to the direction of influence of the variables. Hence, these models are chiefly concerned with the isolation and refinement of causal relationships and tests of lmplications tem and the a pinori theories. endeavors are,
ViS—)—Vis
the observed sys
The objectives emphasized in these modeling
therefore, internal consistency and tests of competing hypoth
eses on the behavioral cc other mechanism driving the system. Forecasting and prediction are important functions of modeling efforts in natural resource economics as in other policy sciences.
Predictions of
price movements, levels for stocks and usage, technology adoption rates, de layed impacts, maximum sustainable yields and similar policy questions are illustrative of the important roles of these modeling approaches.
There is
generally less concern with internal workings than with providing accurate
forecasts in these models.
This is particularly true in situations in which
dynamic models arc coustructed to deji with short-run forecasting proalms (Gross and Ray [1965]).
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Decision problems for natural resource systems have a generally ac cepted set
Ot
Components.
As usually conceived, these problems involve con
trollable and environmental variables, objective functions and structures which relate the controlled and environmental variables to output variables (Fox, Sengupta and Thorhecke [1966]).
The model specified as an optimizing
problem, is used as a basis for policy prescriptions for the system.
As a
consequence research efforts are concerned with both the implications of the optimizing solutions and the accuracy with which the model portrays the sys tem.
When expressed in a dynamic context, these two problems can be produc
tively viewed in adaptive and/or dual control theory frameworks (Rausser and Freebairn [1974a]; Tse [1974]). Decision problems may be usefully grouped into two major types: latory and structural or institutional.
regu
Regulatory decision models are de
veloped for policy questions given a particular institutional and environ mental structure (Haitovsky and Wallace [1972]).
For institutional decision
models, the structure itself is allowed to vary and tius the larger questions on the organization of the general system within which the subsystems oper ate are considered.
Frequently, these connections and identifications be
tween subsystems have been prescribed by physical and economic paradigms (Kuhn [1970]).
An example from economics is one in which time rates of dis
count have been mechanically applied to determine present values.
In the
final analysis, of course, the principal reason for constructing natural re source models is to improve public or private decision-making processes. Fo models to be useful in this regard, their causal or exalanatory proper ties must be sound and tLci foiucast irig on prdictive performance must e reasonably accurot ;.
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2.3
ModeJ.
Eton cuid
Souton Methcd.
A number of alternative ap
proaches for model evaluation and solving for one purpose or another are
available.
They might be characterized as analytical, analytical simulation,
and ad hoc simulation methods.
Although identified as alternatives, it is
important to recognize that the options are simply points on a continuum-ranging from completely analytical (in the sense of closed-form solutions) to ad hoc or exploratory simulations.
The usual approach to model analysis
of systems would involve a combination of experimental methods with some structuring suggested by analytical considerations associated with the prob 1cm. To indicate the framework in which these alternative approaches are em ployed, suppose that the system under consideration has been studied and that a model has been formulated.
Furthermore, suppose that the checks on the
functioning of the model or analog have been performed on the parameters of the estimated model and that the usual tests of predictive capability have been made.
In many situations, even after these stock preliminaries, the
researcher is likely to require further evidence on the adequacy of the model. That is, in addition to these preliminary tests and checks, a more extended evaluation of the model is necessary.
The inconclusiveness of these prelim
inary checks and tests may be due to both model specification and data prob lems.
In the former case, theory inadequacy and the related array of alter
native models present substantial problems.
Checks of logical consistency
and classical statistical tests provide little guidance in such situations. To complicate matters further, economic data describing the system, but not used in the estimation--’.ihicl
itself may involve a nonsysterratic combination
of subjective and observed in forrviti on--are often not available for eva] natiag
17-
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predictive performance.
The application of classical statistical tests in
these situations thus requires considerable confidence in their robustness. The additional evaluations may be performed by one of the three alter Once the researcher is satisfied with
native approaches suggested above.
the corroborative power of the model, the decision analysis based on the model may be conducted, again, through application of one of the three al— ternative methods.
As factors affecting the choice among these alternatives
are in a number of instances similar, the discussion of approaches may be integrated with respect to function.
2.3.1
AnaLc
ciod.
Analytical methods are those using informa
tion ddrived from isomorphic representations of the model structure or closed-form solutions.
Evaluative procedures include those for determining
properties of the models and for attempting to corroborate them with observed or prior information on the system.
Decision analysis methods include the
traditional optimization procedures for static and dynamic models.
The process of evaluation and analysis within this mode proceeds in accordance with clearly defined ground rules.
Methods of mathematical anal
ysis are applied in determining an isomorphic characterization of the re sponse surface for the internally determined variables.
Properties of the
model’s time dimension are inferred from solutions of the difference or dif ferential equations represented.
Properties so obtained arc then compared
to the prior or observed information on the system, summarized to conform to the anlytically obtained results.
This comparison provides the basis
for conclusion:; drawn on the vaii dity of the cor:struct’d model.
•
S ••.
—18-
Once a valid structure for the model has been found, the decision prob lem may be contemplated.
The element required for completeness of the model
at this stage is an explicit utility or criterion function.
With the cx-
plicit criterion or utility function an optimization method consistent with the structural characteristics of the model and objective function is em ployed to derive a solution or str3tegy. 2.3.2
AnaZytteat SZmulcvtZon Me.thodo.
-
These methods maybe applied to
-
models sufficiently complex that exact solutions or isomorphic representa tions for isolating internal properties and optimal decisions are not feasi ble or, as viewed from the opposite end of the aforementioned continuum, when the structure and objectives of the modeling process are sufficiently identified to suggest systcmatized -experimental processes.
Under these con
ditions response surfaces are “estimated” on the basis of outcomes of exper iments designed according to a structure on the externally determined vari ables and parameters.
Properties of the estimated response surface are then
compared with prior and observed information (the latter again summarized in a comparable form) as a basis for corroborating the model.
Procedures which
are, in principle, similar to those suggested for the response surface exam inations are employed for the assessment of dynamic properties. Decision analysis can also be conducted in an analytical, experimental mode.
Information developed through experiments with combinations of con
trol and noncontrollable or externally determined variables, selected according to grid coordinates, may be used to approximate optimal solutions or strategies.
Optistum seek lug or poJ icy Lniprovenent procedures used in con
nection with model experluents may also be viewed as types of analytical
•r
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As before, solution approximations obtained in this manner can
solutions.
be investigated for sensitivity to changes in model structure and criterion functions.
Ad Hoc
2.33
£rmwtLon
a-iod3.
This approach involves evaluation
and decision analysis procedures which are explanatory or are applied with out an explicitly formulated research strategy.
Response surface properties
and dynamic characteristics of the model in this case are usually inferred on the basis of experiments chosen in an intuitive rather than a structured fashion.
Policy analysis proceeds similarly.
Since there is no explicit
objective function, experiments are made with settings of controls, param eters, and levels of externally determined variables which are intuitively based or suggested by past activities within the system.
Policies or deci
sions are then somehow selected (by the policy maker, given his own prefer ence patterns and those of the modeler which are implicit in the selection of the outcomes of the model presented as alternatives) on the basis of the comparative performance of the experiments or simulations conducted. Advantages and disadvantages of the alternative approaches are, of course, dependent on the characteristics of the systems or models under examination.
However, putting aside the capabilities of the research and/or
costs associated with the alternative approaches identified, there are com pel ling reasons for research strategies which maximize the analytical con tent of
the
results.
of Defense critique
This point has beer argued effectively in a D’partmert [1973, pp.
19--221 which on pragmatic grounds suggests
that ad hoc simulations of quant.i tati we models fail to minimize denondence on into it ion in dcc is. i ‘s:a m :ih ing
A s ni Jar
clrgu:e!f
t at a no’c abs rac
t
love
-20-
has been made by Chow [1973b] in developing a conceptual framework for the use of optimal control procedures in the analysis of economic policy prob— ‘ems. The two most important characteristics with regard to types of models are (i) whether or not the model is stochastic and (ii) whether the model is linear or nonlinear.
The choice of research strategy is highly dependent
on these two characteristics of the model.
As demonstrated elsewhere
(Rausser and Johnson [1975]), when models become more stochastic and non linear, the comparative advantage of analytical simulation and ad hoc simu lation methods increases.
One should be careful, however, in concluding
that, just because numerical results can be obtained for these more compli cated models by ad hoc simulation, such an approach is more productive. 2.4 lems.
Mode Use.
Model construction and use are in principle similar prob
For the various model types, objectives of the application can be
specified.
Although this is most natural for decision models, it applies
as well to the other model types.
Because the natural resource systems
models are often large and complicated in structure,
the derivation of solu
tions for applied implications on an analytical basis is not a practical pos sibility.
The result is a procedure whereby the solution is approximated by
experimenting with different predetermined strategies; viz., simulation pro cedures.
Methods for simulating solutions to natural resource systems models
generally range from ad hoc trials to more highly structured procedures in volving numerical approximations and directly e:doying techniques of optimum search and caper imental design; i
.c.
poseful intent of model applications,
analyt ical simulation.
Given the
pur
it is beneficial to systematize choices
..4
•1
-21—
of design points.
This observation follows since the simulation processes
are viewed in an optimizing or control theoretic framework. Sensitivity analysis is simply the process of gathering information with which to evaluate the robustness of particular decisions taken in ap plying models (!4affei (1958]).
Interest is directed to where doubt, uncer
tainty and ignorance are greatest.
Policies very sensitive to changes in
assumptions about which there is substantial uncertainty will warrant skep ticism.
In this regard, a useful distinction to keep in mind is the dif
ference between local and global sensitivity (Zellner and Peck [1973]).
In
a local sense, many models may be insensitive to changes in exogenous fac tors, parameters, etc., but very sensitive to such changes in a global sense. Selecting the trials or experiments to be conducted in a sensitivity exami nation for particular policies involves a choice between ad hoe and formal experimental design settings (Hufschmidt {1962] and Hunter and Naylor [1970]). Application of experimental design methods to probleis of model sensitivity have recently received increased attention.
Naylor (1970], Ignall [1972),
Naylor, et aL. [1967], and Zellner and Peck [1973] are illustrative of these methods and the types of results that can be obtained. designing the related experiments have been routine.
Methods employed in Complete factorial ex
periments are by far the most common, although more sophisticated designs can be employed (Kleijnen [19741).
The advantage of the more specialized
design techniques is that trade-offs are known in advance (Handsconb [1968]). Since it is known in advance which hypotheses are maintained, the testable features of the design should bc chosen accordingly (John (1971], Mondenhall [1970] and Kleijnen [1974, 1975]).
Response surfaces are simply functional relationships between param eters, environmental variables, structural choices, and perhaps, criterion functions and internally determined variables (Naylor and Budrick [1969), Box [1954], Burt [1966, 1967, 1964], Hufschmidt [1962]).
Such surfaces are
useful in applying models for several purposes; especially forecasting and decision uses.
As with sensitivity analysis it is important to recognize
that when such relationships cannot be obtained as closed-form solutions, numerical approximation procedures must be employed.
The more recent work
on response surfaces dates from important papers by Box and Wilson [1951] and Box [1954].
These and related works contain clear statements of the
approach to response surface examination and sequential experimental designs (Davies [1954], Hill and Hunter [1960], Chernoff [1972]).
Less structured
types of procedures are due to Box [1957] and Box and Hunter [1959].
These
designs explore response surfaces by first estimating them for restricted regions and then moving to estimate other regions on the basis of the infor wation obtained.
In a related context, a number of policy improvement or
optimizing techniques are available (Emshoff and Sisson [19701).
These often
involve sequential designs which begin with an extensive search via simple exploratory experiments arranged so as to converge towards some peak (or valley) of the surface and subsequentlr switch to intensive search methods as the optimum is approached (Cochran and Ccx [1957], Mihram [1972], and Conlisk and Watts [1969]). The connection between response surfaces and solutions to resource sys tems models is easily seen when it is recognized that the surface may be de fined in terms ot the app iLcat ton ohective. obj ectices are easily determined.
For deciston problems, these
For forecast
‘ig,
behavioral and descript I ye
•
.
-23-
models application objectives are generally specific to the problem at hand. Since natural resource research is undertaken with a purpose, the uses of response surface and sensitivity analysis techniques in achieving this pur pose are obvious once it is formali:ed.
Moreover, it should be apparent
that an optimization problem is implicitly involved in all model applica tions.
b ... I
-24-
3.
It
ural
was
indicated
resource
from most
SPECIAL PEATURES OF RESOURCE SYSTEMS AND POLICY PROBLEMS
systems
other
earlier
and
economic
that
policy
models.
there
arc
problems
These
certain
which
included
characteristics
combine
to
of nat
distinguish
complexity,
external
tteta
ef
fects, long planning horizons, and problems of information bases for struc
•
tures and initial conditions.
Sonic elaboration and further enumeration of
the special characteristics of resource systems and models are presented in this section. 3.1 •
Re6ouisie Sy6tcmo.
As previously noted, natural resources are typically
regarded as renewable or non-renewable (exhaustible).
Each of these classes
of extractive resources possesses its own peculiar characteristics relevant to the topic at hand.
These are treated sertatim below.
Fisheries, forests, and water serve as examples of renewable resources; resqurces which exhibit economically significant rates of regeneration.
Fol
lowing the lead of Peterson and Fishor [1976], we usc fisheries to illus trate the distinguishing characteristics of the renewable resource.
While
Clark and Munro [1975] highlight the resemblance of fisheries models to mod em capital theory, there are critical differences as well.
The first pecu
liarity of models involving biological species related to their natural re generation processes, or biological growth functions.
Thus, extraction of
these resources differs from other production processes since yields in any period influence subsequent yields by changing the stock of remaining re sources.
Indeed, production functions for a single renewable resource typ
ically include three factors:
time, to allow for technological progress;
some measure of effort (say, fishing); and resource stocks.
Much of this
hr.
-25-
literature is of the exploratory type, since the production functions in this class of natural resources literature have Ieen assigned all sorts of functional forms, with justification seldoLl provided. In response to questions like: ing effort?
(1) What is the optimal rate of fish
(2) Does this rate correspond with maximum sustainable yield?
(3) Will extinction occur under normal conditions?
(4) Is this bad?
(5)
Does optimal behavior correspond with behavior under a competitive regime?,
some of the most intricate and interesting models in economics have been de veloped.
These models exhibit multiple equilibria, involve dynamic optimi
zation, recognize externalities,’ and examine resource exploitation under various institutional structures and policies. Another distinguishing characteristic of natural resource models is the presence and importance of the user cost concept--the decrease in the value of an asset associated with use.
In the fisheries example, the margi
nal user cost (shadow price) of fish in their natural state is the quantity by which t1e present value of the fishery at that point in time is diminished by the removal of one unit of the fish resource.
This quantity is not gen
erally observable, but rather must be imputed using present and projected prices, technologies, and stocks of the resource. The prevalence of the common property status and problem is a further
distinguishing characteristic, which interacts with and magnifies some of the other peculiarities of natural resources problems.
Gordons
[1954] sem
inal paper on this subject shows that in the absence of cooperative agree men ts, firms in a ccnaon property fishery will enter and cxi drive rents to zei’n in the nroce.zs user costs assoc ated with depleti
.
t freely and
Congos tine ext:rnaI ties created and fish stks
e iyorod by the
4
individual firms, generally resulting in greater effort and lower stocks than are optimal. More formally, the essence of the renewable resource use problem can be illustrated with a simple model of a single biological species.
The type
of illustration which follows is generally attributed to Schaefer [1954] and is rather widely used in recent natural resource economics literature. assumes that the rate of change of the species stock,
It
is a function of
the current stock: (1)
g(S),
such that g(S) has two roots; viz., the species stock is in equilibrium =
o]
at S
=
Se; the minimum biologically viable species stock below
which extinction would occur, and at S sustainable by the environment. between S
e
and S
the species.
m
=
Sm the maximum species population
The functional
and is maximum at S
S
,
is positive for stocks
the maximum sustainable yield for
It is worth rioting that a fairly sizable amount of literature
has been devoted to showing why when S is the maximum rate of exploitation
of a species that can be sustained indefinitely, it may not he the economi cally optimal rate of resource use. Since the extraction of renewable resources involves an instance in which current yields affect future yields by altering the remaining species stock, it has become cormuonplace to usc a production function to describe the extractive
rocess.
This function generally takes the form f(E, S, t),
where E is an index of capital,
labor, and other input quantities used in
extraction, and referred to simply as effort, and the presnnce of time, t, allows for the possibility of technical progress.
The inclusion of S is for
27—
the reason suggested above, and when the resource is a conmon property this presence leads to inefficiencies and conflict. The present value of the resource can then be expressed by the integral:
(2)
f
[pf(E, X, t)
dt,
wEje
0
where r is the discount rate and p. w are respectively output and effort prices assumed constant (competitive product and factor markets).
This
present value is then maximized subject to the system equation: (3)
=
g(S)
-
f(E, S, t),
and side constraints that Sm
>
S
>
0 and E
>
0.
For this, it is necessary
that the current value Hamiltonian: (4)
H
=
pf(E, S, t)
-
wE
+
?[g(S)
be instantaneously maximized, where
-
f(E, S. t)J
is the marginal user cost of the
species in its habitat; i.e, the reduction in the present value of the
species at time t occasioned by the removal of an eddt.ional unit of the species. To maximize (4),
the partial derivative with respect to the control
variable, effort, is set to zero: (5)
HE_pfEwAfEO.
Clearly, price (p) equals marginal extraction cost (w user cost (A).
plus marginal
The presence of the value A in this condition then clearly
differentiates this case from the optimizing conditions with non-eatractive commodities.
To maximize the present value of the res urce (2), it is also necasarv that the t inc path of
be po’errwd b: the di Fforenti a 1 eq :at ion:
_t_
(6)
-
=_H÷rA=_pf_ Ag+A f+rA
This equation provides that the capital gain from an additional unit of the species
[J
plus the marginal revenues generated (p
the additional growth (A
plus the value of
equals the user cost of the extra output gen
erated (A f) plus the opportunity cost of the natural species (r A).
If
not, if the species were more or less attractive as compared with other in vestments, then the price A would be bid up or down by the investors. Models of non-renewable resources, like oil, coal, and minerals, also possess a number of distinguishing characteristics.
Frameworks for these
resources involve optimally depleting a stock, with no significant natural regenerative possibilities and recycling (artificial regeneration) limited by economic as well as natural processes.
For this reason, the theory under
lying these models have been termed “theory of the mine”. One characteristic for this class of resources which is similar to re newable resources but not other production processes is that user costs should be considered alongside extraction costs in deciding stock depletion rates.
That is, for non-renewable resources user costs (determined by the
future time paths of prices and costs) represent an endogenous depreciation cost as contrasted with the usual notion of depreciation which depends
only
on the passage of time. The essence of the exhaustible resource extraction problem can be il lustrated by a simple model.
For comparison with the renewable resources
problem we again adopt the production function aporoach of Peterson and Fisher [1977j ra Lher thaii the cost func t ion models of Gordon [i967 and Cu:i— mings
[1969].
-29--
Using the same notation, yield for a pactcu1ar tract, f(E, S. t), de pends on effort, time, and stock oF remaining resources. has its initial stock (S ) 0
At t, the tract
less cunulative extraction; so that
t
S(t)
=
0 S
-
J
Y(’) d y
0
For the exhaustible resource problem, the conditions are the same as for the renewable resource model except for the biological growth function. Denoting again by p and w the prices of output and effort, value integral,
(3) is the system equation,
(2) is the present
(4) is the Hamiltonian, and (5)
and (6) are the necessary conditions, where g(S) is omitted from each equa tion.
The interpretations are similar as weli.
For example,
(5) determines
the rate of mineral extraction and (6) provides for an adjusting A which maintains the attractiveness of mineral stocks equally with other investment goods.
If exploration is important in a particular exhaustible resource, models of extraction becme more complex (Koopmans Fisher [1976]).
[1973], Peterson and
There are numerous motives for explorat-ion, of course.
Monopolists may wish to discover deposits in part to raise barriers to entry by keeping these stocks out
of
the market.
Alternatively, firms may devote
too few resources to exploration due to the uncompensated external benefits of
the information they supply others in the process. While uncertainty is not exclus ve to the domain of natural resource
systems, it is difficult to imagine areas in which uncertainty play’s as large a role as, for example, drill ing decisions for oil aud natural gas. The uncertainties of supIv—— iocation, quant itie
,
qucli ty-—cre enoruous
The rather substaut Ni ‘o1sre of reat literature on bN’ ira; models 1
is
-30-
relevant here.
A potential lessee of a mineral bearing property wishes to
know its worth and how much to pay. a bidding strategy is involved.
When the price is determined by auction,
Recent studies to assess the implications
of factors such as number of bidders, whether bidders collude, and whether bids are open or closed include Wilson [1075], Williams [1075], Gaskins and Vann [1975], and Leland [1975].
One interesting suggestion from this work
is that asymmetries in information among firms can lead to inefficiencies
and that often prospective lessees are led to inefficiently gather excessive duplicate information to reduce uncertainty and gain an edge in sales of leases.
There is strong evidence of this phenomenon of excessive informa
tion gathering preparatory to development of the U. S. outer continental shelf. In addition, since the value of a stock depends on the stream of future prices, there are substantial uncertainties on the demand side as well. But this is just the beginning--uncertainty as regards future demands is compounded by the fact that substitutes and new techr1ogies nay develop (Dasgupta and Stigiitz [1975], Peterson and Fisher [1976)). One type of substitute for some of these extractive resources is repre sented by the secondary materials from recycling.
Some have argued (e.g.,
Weinstein and Zeckhauser [1974]) that in the absence of externalities asso ciated with waste disposal, the free market results in optimal levels of recycling activities.
However, such absences are not often in the real
world and thus these externalities are clearly important and should be taken into account.
Since
recycling
haustiblc resourccs and
in
acts in both the role of substituting for cx
reducng
pnllut;on, failure to recognize thcse
externali ties leads to an under-allocation of resources to the recycling
-31-
activity.
We will return to this link between extraction and the environ
ment below. A characteristic of some of the most recent contributions to the liter ature in extractive resources is that rather than operating from the para digm of the behavior of a firm Out to maximize the present value of a re source, they presume the view of a planner seeking to optimize some more
broadly conceived social welfare function. generational welfare.
Questions arise concerning inter
Should utilities he discounted?
How can we justify
depriving one generation because of a greater gain to another? consequences of the Rawis
What are the
[19711 notions of distributive justice wherein a
“maxi-min” criterion is adopted, where social welfare is established on the basis of the least privileged generation, for growth, capital formation, etc.? Finally, a distinguishing characteristic of models of natural resources is the importance of information from other discipi ines. Fisher
As Peterson and
[1976] suggest, economists presently employ geological and engineer
ing information in thei
natural resource models and recently “there has
been a flurry of activity”. Bradley
Examples include:
[1967], Kuller and Cummings
Franklin Fisher [19641,
[1974], and iacAvoy and Pindyck [1975,
pp. 65-79]. In brief, renewable and non-renewable natural resources have special characteristics which distinguish them from other economic processes, which stimulate different problems, questions to be posed, and give rise to more complicated modeling efforts. tute
zjvcn
If a resource is exhaustible, hut has a close
curreit or fcrseen tecnoior, is it appropriate to dis
cuss po icy problens in iie iiari or.
coNx
of i’xhmmstil i
i:yt
Is the net
;f.
32
effect of technology to make primary factors more suitable, as would seem to be the case for energy resources? The problem of changing resource concepts is also real.
Scarcity of
natural resources is a function of current technology as well as many other social factors which are not economic in nature.
As societies evolve, the
focus on particular primary inputs for production may change. ent policy models accommodate these types of shifts?
How do pres
Finally, natural re
source issues cannot be intelligently analyzed without reference to common property problems and external effects. That this discussion suggests is that natural resource models are grossly incomplete representations of the systems they attempt to duplicate. Most ignore the substitutability problem, evolving production and consumption decisions, and numerous externalities of production and consumption.
The
models though complex and including economic, biological and physical compo nents are generally.oversimplified.
Given their future looking orientation,
current perspectives on model adequacy and even the characteristics of nat-. ural resource problems may change.
In fact, changing model structures for
system representation and policy preblems would seem the usual situation rather than the exception.
This means that models must include provision
for reflecting these possible changes ana for updating.
.
..‘
.,:...
-33.
4.
RESOURCE SYSTEMS APPLICATIONS:
A REVIEW
In the previous sections systems methods were defined , categori:ed and discussed and natural resource economics frameworks were characterized with special reforence to identifying those special character istics which distin guish these problems from other economic models. •
The present purpose is to
provide a flavor of the range of applications of systems methods in natural resources.
Reference is made to studies which employ simulation methods,
analytical optimization, and analytical simulation.
The critique of this
literature is reserved for Section 5. 4.1
SimuZatLon.
In natural resources frameworks, as with other types of
models, the modern applications of systems concepts and simula tion methods have much historical significance.
Furthermoro, in contrast to the impor
tance of.simulation in the early development of other model s, the emphasis in the resource literature was .illitially on the concept of a system.
Systems
concepts, growing out of the physical aspects of the probioms studied and the engineering literature, found a very natural application in studies of resource problems. Systems and simulation applications to natural resource and region al development problems often involve the public sector.
As Kain and Meyer
[1968] have noted, simulation is particularly useful when evaluating invest ments characterized by important externalities, broad social objecti ves and durable installations.
When we add to these features, the importance of un
certainty, technological change, research and development strategies , and the sequential aspects of :t.tural resourc’; decision-making, compu ter simula tion becomes on even mon appealing tool (R:iusser and Dean [1971a , 1971b1).
—34-
In a mechanistic sense, models oF resource systems are generally dy namic and nonlinear.
Some nonlinearities are fairly substantial including
those involving artificial, time-counter relationships.
Dynamic structures
of these models are often characterized by lagged internally determined and conditioning variables and are represented by a system of difference equa tions. form.
Approximately one-half of these models are simulated in stochastic Most stochastic simulations are limited, however, in the sense that
only additive stochastic (disturbance) elements are recognized, i.e., only first moments of sampling distributions of the structural parameter estimates arc used.
A large number of the stochastic simulations were developed for
the physical models representing hydrologic phencmena. In Table 1, a number of empirical studies are described in terms of the authors, the situation modeled, objectives and decision variables.
Reported
model characteristics include model type, type of simulation, computer lan guage used, validation procedures, and information on whether the model is dynamic, stochastic, and nonlinear.
For the most part, the table is self-
explanatory with respect to the listed characteristics.
The three charac
teristics for which the conventions adopted may require elaboration are validation, ty-pe of simulation and the competitive versus non-competitive classification for gaming models. process are active and passive.
Terms used to describe the validation All researchers are, of course, concerned
with corroborating model representations with systems and, in fact, are prob ably imnlicitly doing such at all stages of the construction process.
Such
implicit corroborative activities are described as passive validation in the tabled information on the studies sur’.uvJ.
Stud i in which cue corroboran on
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FORTR’tN
FITII’tPAh
tempo icr
30-
processes are more systematic and for which results of tests and associated procedures are reported are classified as active validation processes. Simulation of the models are classified as historical, ad hoc, and de signed.
Historical simulations refer to experiments with models in which
the conditioning variables a-re entered as historical data series.
Ad hoc
simulations refer to experiments in which the design points (values for con ditioning variables, parameters, etc.) have been chosen in an intuitive or non-systematic fashion.
Designed simulations are those in which the exper
iments with the models have been developed using an experimental design. This implies the inclusion of an implicit or explicit response or objective function and the choice of a method of selecting design points which will produce the information required to identify the associated relationship. It should also be noted that in the decision variable column we report for behavioral arid forecasting models the variables (endogenous) which refer to actions taken by the behavioral units while for decision models we report those variables (exogenous) which refer to policy actions that might be taken by public or private decision-makers.
Second, the procedures for clas
sifying models as linear or nonlinear are arbitrary; some models in which only weak departures from linearity exist are classified as linear models. Third, in the fifth column we classify as stochastic those models which are simulated stochastira liv and not constructed models which incorporate sto chastic elements.
Last, for the computer language designation we classify
all simulation models for which the computer iaguagc is not reported or it was not possible to Siroiiatiu: ex1)rJ souhisticated
t’nIa
fr
ofer the actu I computer langsage util ized as Fortro. LOtS
or Jus I rescs(’ node] s are tynical iv more
ober cr,z)iirsT:,ece]s.
1nhrr of- factorial and
-40-
factorial-factorial designs have been employed to examine response surface questions.
Some designs also involve optimum seeking methods.
procedures, however, are less precise.
Validation
Only eight of the surveyed studies
went beyond graphical comparisons of sample or historical and simulated values of selected output variables.
Predictive properties of the models
were typically neglected in corroborating them with the systems in question. The models specified in Halter and Miller [19661, Hufschmidt and Fier ing [1966), Hamilton, et al. [1967), Dudley, et al.
[1969), Rausser, et aZ.
[1972, 1975), Jacoby
[1972), and Chow and Kareliotis [1970) are viewed as
representative of this group and are selected for further discussion. first three models concern river basin systems.
The
The Halter and Miller model
represents an early application of industrial dynamics to water resource de velopment projects.
Proposed projects are dam construction and channel im
provements in the Calapoola River Basin. control, fishing, and drainage.
Benefits included irrigation, flood
A particularly interesting aspect of this
model was the treatment of the temporal distribution for hydrologic flows. These flows were generated internally in the model by a random number gen erator process.
Considerable care was taken in attempts to assure that the
simulated hydrologic data conformed to historical flows.
The experimental
design used for the decision problem was reasonably simple with no indication as to how the combinations of project size and operating rules were selected and evaluated. The Hufschrnidt and Fiering [19661 model is more general than the one advanced by Halter and Miller.
This study presents the steps and procedures
for a simulation program including aspects related to collecting and organ izing hydrologic ad economic data.
An interesting de]opmcnt foc
-41a
synthesizing hydrologic events is provided. with abatement costs.
Pollution is considered along
For decision applications, economic consequences
(benefits and costs) associated with design variables and outputs were eval uated under several assumed interest rates, static and dynamic investment patterns, as well as different discounting methods.
An explicit criterion
function was specified, a few basic plans were investig4ted and, from knowl edge accumulated, improvements were made upon the basic plans and the search continued. The third river basin study conducted by Hamilton, et at.
tains more of a regional flavor than either of the other two.
[1969], con The principal
objective of the work was to advance the state of the systems simulation art for regional analysis, particularly where social and technological factors
form an integral part of the system under examination. of this model are:
Important features
(i) inclusion of demographic and economic components in
a single model; (ii) explicit application of economic and engineering con cepts to regional water resource problems; (iii) dynamic aspects in the form of feedbacks and lagged variables within the various components as well as between components; and (iv) ability of the model to facilitate sensitivity analysis.
One of the more interesting results of the simulation analysis
was that water shortages emanate not from the scarcity of the water resource itself but from current water treatment, storage, and distribution systems. Turning from river basin applications, recent studies by Rausser, et at. [1972], Willis and Rausser [1973] were advanced in an attempt to determine the proper level of public subsidies fur water desalting plonts, the invest ment levels and sequeTicing of various writer source developmrnts, r’nd the allocation of water across different use sectors.
Bases for the public
e:
II
•1 .
V
-42-
subsidies are the external benefits which result from “learning” or knowl edge accumulation of desalting techniques.
Experience gained in the con
struction and operation of a particular desalting plant is presumed to lead to more efficient production for future plants.
Since it was not possible
to derive the marginal density function for benefits analytically, computer simulation experiments were employed.
Given the approximated external bene
fit distributions, appropriate levels of public (state and federal) sub sidies were derived for alternative sets of assumptions.. The model developed by Jacoby [1967] emphasizes alternative investment and operating decisions for electric power plants in West Pakistan.
Poten
tial investments in generation facilities for each of several electric power markets are analyzed. power demands. fied.
Each plan. was constrained to satisfy predetermined
Associated temporal patterns of operating coSts were speci
The computer simulation model generates outputs of various plants,
ranges of fuel prices, transmission constraints for each year, the distri bution. of foreign exchange rates, and the distributioa of opportunity costs of capital.
The opportunity cost information is particularly important
given the multipurpose nature of hydroelectric and.irrigation developments in the regions investigated.
Experimental designs employed in this simula
tion analysis involved both multistage techniques and partial factorial de signs.
On the basis of a single basic demand projection, a variety of plans
were tested, some of which were eliminated from further analysis.
This ini
tial analysis provided a new set of combinations to be investigated.
Unfor
tunately, no real attempt was made to validate the constructed model. The Dudley, at at.
(1972] model was intended to determine the “best”
area size for irrigation.
This decision is presumed to take place in
-43S
conjunction with a reservoir of a given capacity.
The specified criterion
function involves a twenty-year planning horizon, net revenue derived from irrigated cropland, net revenue derived from dryland crops, and fixed costs The actual effects of varying acreages were determined
of capital items.
by simulating over a twenty-year period, for both stochastic demand and sup ply structures.
Sensitivity analysis was employed in an attempt to deter
mine how the selected acreage should be altered under varying opportunity costs.
No attempt to verify the constructed model was advanced and the ex
perimental design is simple. 4.2
AnaLyticaL OptAmL:atAon.
Many applications in natural resource systems
have used analytical optimization rather than simulation methods.
We list
below some examples to illustrate the variety of problems addressed and make only general remarks about the groups of applications. In the renewable resources class, in additiqn to the burgeoning num bers of studies of optimal rates of exploitation of fisheries (e.g., Bell [1972], Mohring [1974)), the biological growth functions discussed earlier have been incorporated into empirical systems models to address waterfowl management issues, forests, game animals, human populations, and even insects and bacteria.
For example, Brown and Hammack [1972, 1973, 19741 use dynamic
programming procedures to suggest management schemes for migratory waterfowl, Beddington, et at.
[19751 develop a model to reveal optimal rates for har
vesting deer, and Spence (19731 studies the blue whale.
The Spence paper is
an excellent example of the use of the calculus of variations to suggest op timum regulations for an endangered species.
After estimating a growth equa
tion and a production function for blue whales, Spcnc’e dopts the present
S
-44S
value of the differences between the market value of the blue whales har vested and the associated costs as the relevant criterion.
Calculus of var
iations is then employed to find the best intertemporal patterns for whale harvesting and the economic value of the resource when these optimum strat egies are adopted.
In brief, the optimum strategy was to forbid blue whal
ing for some period of from seven to twenty-one years (depending upon cost assumptions). Applications to water are the most ubiquitous of all.
Examples include
Cummings [1971] and Burt [1970], who examine optimal conjunctive use of round and surface water; Dudley and Burt [1973] who idvance a stochastic dynamic programming model for reservoir management purposes; and Rausser and Willis [1976] and Armstrong and Willis 119771 who combine integer and nonlinear programming procedures to determine both the sequencing of water resource investments and water allocations.
The paper by Rausser and Willis
serves as a useful example illustrating methods of resolving several of the more important problems in the design of water resource systems which have been neglected in the literature.
Their framework includes a method for
dealing explicitly with technological progress (in this instance, learning and new desalting processes), with staging and sequencing of multiple supply sources, with the simultaneous selection of rate of investment in the cap ital complex used to exploit the resource along with the allocation of this water once the capital complex is in place, and price sensitive demands for water.
In a modeling context, we have found that generally more titan two
of these issues arc explicitly addressed; the others are simply neglected. However, it is den that each of these issues p):3y5 an inportant role in the design of water resource systems and sknzld he formally exanined.
The
•. I
Cd.:’
-45-
paper advances a decision framework for solving large-sc3le investment se quencing and water allocation problems, formally demonstrates the robust ness and convergence properties, and applies the framework to an empirical situation in California. As Peterson and Fisher [1976] conclude, these models, particularly for the biological species, are limited as management tools largely
“...
because
their functional forms are too simple and their empirical content too low”. Owing to the weakness of the data base, parameters of growth and production functions are not known with any degree of precision.
The need for an ex
panded data base is suggestive of the potential value of improved coopera tion of economists with natural scientists. Another weakness in this empirical work is that these studies of renew able resources are often not based upon dynamic models.
Other studies, al
though based on aspects of a dynamic growth concept, use static optimization methods to derive policy implications. as examples of this approach.
Mobring [1974] and Bell [1972] serve
Only a few of these ap!lications are fully
dynamic (e.g., Brown and Hammack [1974]). In the exhaustible resources category, a number of approaches have been taken.
Much of the early work (Barnett [1950], Landsberg, et at. [1963],
Schurr and Netschert [1960]) was based on the input-output model, although it was not until 1972 that the first full scale input-output model was used to forecast mineral demand and compare these with reserves (Ridker [1972]). Econometric procedures based upon macro-economic growth models were used by Hudson and Jorgenson [1974] and by MacAvoy and Pindyck [1975] to estimate demand and supply for tnergy sources in the Uniter) States.
•
S
-46-
Indeed, for this class of resources, unlike the renewable resources, the empirical applications do not explicitly model long run optimizing be havior.
Presumably, it is the difficulty of solving realistic cases of
many variables, the presence of inequality constraints, and the exaggerated assumptions made necessary to obtain estimates which has led to a propensity to use linear programming and.similar models.
An example of these types of
applications in the field of energy is provided by Nordhaus (1973]. 4.3
AnaLytical S2matatLan Mc.thocto.
Recent applications which follow an
earlier suggestion by Dorfman (1965] to combine the use of analytical optimi zation and simulation methods, include the models developed by Jacoby and Loucks (1972] and Dudley and Burt (1973].
The first study involves construc
tion of a river basin planning model where the number of available develop ment opportunities is extremely large.
To analyze the resulting framework
in a tractable fashion, these authors employ analytical optimization models to screen the set of possible plans and select a smaller number fot detailed simulation analysis.
Stochastic aspects of the problem are explicitly rec
ognized both in this study and in the Dudley and Burt model.
The Dudley-Burt
model, following the earlier work of Dudley, et at. (1972], uses a simulation model to compute state transition probabilities which in turn are utilized in a stochastic dynamic programming model to determine optimal:
(1) inter-
temporal water application rates; (2) abandonment of irrigated acreage for the remainder of the season; and (3) the acreage to plant for potential irri gation at the beginning of the season. Marine’s work provides another useful example of the incorporation of technical progress in a decision model and the exp]icit recognition of
-47-
uncertainty.
He concentrates on one of the many important aspects of the
energy problem--viz.,
the race between development of breeder fission arid
the economic exhaustion of natural uranium resources.
His approach involves
the use of sequential probabilistic linear programming to define optimum electricity plant-mix decisions during the 1930’s
(the planning horizon ex
tends through nine S-year periods through the year 2025), given the uncer tainty surrounding the date of availability of the breeder reactor and allow ing for the possibility that future shortages of uranium resources will cause an increase in electricity prices and this to a reduction in demands. The approach provides a good illustration of the analytical simulation method
since a decision tree was structured and used to screen the range of possible options and hence to enable the development of a linear programming formula tion for solution of the decision problem.
An interesting result of his
analysis is that early decisions are not very sensitive to distant future uncertainties in this instance, and relatedly,
there was ar ather low value
of information attached to the date of availability of the resource-saving breeder technology.
These results are connected with the adoption of an
assumed ten percent discount rate.
Other results suggest that the U. S. has
enough stocks of coal to enable electricity generation from this exhaustible fossil fuel until well after the 2025 horizon, so that coal is regarded as a “backstop technology” for the event of failure to achieve a safe and com petitive breeder.
Further, by this date the chances are good that either
fusion or sol or energY will he on— 1 inc in a large scale, so that no tural re source scarci ties are not scn by Hanne as a hot tieneck to the e ectricity sector and are then not ‘‘e:ocn t ia 1 ‘ 1 halts to ac:; th
-48-
The above natural resource models are generally advanced relative to their counterparts in other application areas, particularly as regards their detail and the methods employed in using simulation for decision analysis. However, they might be characterized as often deficient in terms of model validation and theoretical foundations. not an unexpected result.
Owing to their complexity, this is
A trend of recent vintage that will hopefully con
tinue and experience further growth is explicit recognition of risk and un certainty.
Illustrative applications of these efforts may be found in the
occasional staff paper series of the World Bank (e.g., Pouliquen [1970] and Reutlinger [1970]).
Applications of these methods along with other approaches
to uncertainty in a water resource context are treated in Rausser and Dean [197ia,
197lb].
‘hi.,,
-49-
5.
CRITIQUE AND APPRAISAL
The impact on models of the natural resources of the modern development of systems analysis and simulation techniques is apparent.
New and ambitious
approaches to problems posed in thc context of existing paradigms and explor atory work with less confined constructs have been stimulated by the develop Grappling with the difficulties
ment of systems and simulation methods.
presented by applications of this highly flexible approach and attempting to refine them has and should continue to provide resource economists with the basis for a stream of useful results. Advantages provided by the use of systems analysis and simulation can be more fully exploited if the two processes are themselves more systemati cally employed.
Moreover, the appropriate framework to be utilized as a
basis for systematizing the processes of model construction and use appears to involve concepts of stochastic control.
In what follows, we describe the
stochastic control process in its most general context, establish the link between model construction and application with control as the unifying force, and offer an assessment of some promising avenues for future modeling efforts in natural resources. 5.1
Stochastic Conaol.
Stochastic control problems involve:
(1) Specifi
cation of the relevant decision maker(s) and the control or instrument vari ables available for manipulation.
Decision points and procedures for revi
sion of policy actions in the light of new information are also important to this component of the specification.
(ii) Specification of an objective
function, possibly as a representation of collective prefccences, which ranks the different states of the system.
Arguments in this function are key
:
-
.
-50-
performance variables, including those endogenous and controlled variables considered by policy makers to have important implications for the problem under study.
(iii) Specification of constraints or a policy possibility set.
which includes (a) state .tranáformation functions relating the internally determined variables in each period to the policy variables, other exogenous variables, and lagged variables describing previous states of the system, (b) initial conditions for the system, and (c) other constraints delineating the feasible control variable and endogenous variable spaces.
(iv) Specification
of the processes of information generation, together with prescriptions for the analysis of data by policy makers as the decision sequence proceeds. The latter embraces active learning processes whereby the additional infor mation may be used to lessen initial uncertainties about objectives, the constraint functions, and states of the.systern. Stochastic control methods are thus dynamic optimizing procedures (ap plied to multi-period decision problems) in which imperfect knosledge is a key characteristic.
Usually a discrete-period, sequential decision making
process is assumed.
In each decision period, a maximizing policy is se
lected from a set of feasible actions.
The constraint functions delineate
the feasible policy space and specify the endogenous variables included in the objective function conditioned on instrument, environmental or condition ing variables, and the initial state of the system. Stochastic dual control methods explicitly recognize that as a system progresses through the sequence of periods, data become available which can be used to update or revise the decision-maker’s perception of the policy possibility set.
These revisions, in genera], should not be regarded as
separate from the derivation of an optimal policy.
Alternative policy
I.’ .,
C
-51‘I
decisions way reveal more or less information about the system.
Inherent
benefits of the additional information depend upon whether or not an “im ’ representation of the structure results in superior future control. t proved Costs of such information emanate, in part, from choosing a current policy which is less than optimal from a pure control point of view.
The important
aspect of this approach, from the standpoint of natural resources, is that the dual feature admits an experimental component which robes the system to learn more about the nature of reserves, structural growth or biological yields, the effects of technological change and the like.
For this probing
component, formal experimental procedures must be designed to determine whether the losses associated with current decisions can be recovered in subsequent Periods by utilizing improved information on the structure
5.2
Contwt, Model Conot’wctton and AppfA.co_tion.
As the foregoing discus
sion would suggest, the separation of model construction and application pro cedures is in some respects artificial.
Models of nvtural resource systems
and the systems themselves evolve through time.
Applications of the models
are made on an ongoing basis for policy and information purposes.
Tho se
quential process of model revision application, revision on the basis of added information, is obviously one which lends itself to the stochastic con trol framework. Methods for applying techniques in the
construction
and application of
natural resource models are at present, and p:’obably will remain, available in an analytical context only for overly sia.plistic models.
This does not,
however, preclude the use of dual control principics in more realistic situa tions.
Fron an operatic’nal viewpoint, an tmpert:tnt issue in application or
-52--
model use is to understand the sequent ml nature of the model development and solution process.
Specializatiorus of applied models for use in design
ing search and revision strategies (models of models) are suggested as use ful in this context.
So are methods for more completely investigating in
formation generating processes, which arc, or should be, very much a part of natural resource modeling because of the large amount of uncertainty existing regarding model specification.
The list of such techniques in
cludes preposterior analysis (Raiffa and Schlaifer [1961), Anderson and Dil ion [1968]) and artificial intelligence (Meier [1969), Shubik [19601).
The
two techniques, in an applied context, involve selecting solutions to gen erate increased information on the model structure, perhaps at some expense in terms of net benefits in the current period.
5.3
PtotnLug V-ou.
One of the much emphasized attributes of systems
and simulation methods relates to the use of the approach as a substitute for more expensive and/or larger scale physical experimcuts.
Within the
adaptive control framework, problems resulting from attempts to formulate and investigate such models have a natural criterion function.
That is,
maximize the information content of the results less costs of complexity, given physical, institutional, time and budget constraints.
Policy or con
trol variables for problems formulated in this context are, however, less apparent.
At present they would seem to he discrete types of choices such
as methods of parameter cat iraation, the 1 comp exity of the model
,
scale of
prototype, choices of paradigm, verification procedures and the like. Choices of control variables would, of course, vary with the problem being studied and the Purpose of the modc-i
md
exercise.
.1
••
a •a
-53S
An interesting method for handling problems of this type is the pre posterior analysis developed by Raiffa and Schlaifer (1961].
Viewed in
connection with biological growth function estimation, this approach pro vides a means of more effectively positioning actual physical experiments. As a consequence, model complexity and the cost of the physical experimenta tion can be reduced.
In this exercise the control variables relate to the
extent of preposterior analysis and choices of physical experiments based on such information.
Although not fully exploiting the sequential nature
of such problems, the structured approach advanced by these authors has wide areas of potential application.
Surfaces generated by criterion func
tions in decision models, predictive performance functions, and measures of appropriate behavior characterization can obvious]y be viewed in a response type framework.
Accordingly, the associated response functions can be ex
plored at least conceptually, using methods of preposterior analysis. A promising application of systems cbncepts and models is in the de velopment of artificial intelligence.!’
These models attempt to recreate
to decision-makers’ thought and discovery processes, rules of thumb applied complex real world systems, intelligent behavior, and effective problemsolving or search methods.
They embrace a philosophy for approaching prob
lems heuristically rather than with an organized and definable set of tech niques.
For many problems not solvable by classic mathematical and stat is
tical models, these methods may be useful.
They involve attempts to move
(Kuehn towards opti;aum solution procedures rather than optimal solutions and Hamburger [1963)). as Although sysL ems models and all ted techniqucs were suggested early mc:ns fur gencratizag information
abtut economic systewa (Sinon and Nerve] 1
-54-
[1958]; Shuhik [19601; Clarkson and Simon
[1960]), related heuristic pro
gramming and learning constructs have received little attention by agricul tural economists.
The process of constructing and simulating any model of
a system can be viewed loosely as a process of developing artificial intel ligence.
Hence, the observed lack of associated applications is based rnainiy
on the absence of formal consideration of these processes. The connection of these processes with the theory of learning (Bush and Estes
[1959]) is apparent.
Heuristic programming and learning theory have
been most popular in the study of games (Shubik
[1960]).
However, they have
wide potential applicability in exploratory research associated with the eclectic models employed in agricultural economics. of view and in i-elation to decision models, problem.
From an economic point
learning theory is an allocation
Hence, appl ications of heuristic progiamrning and the generation of
artificial intelligence fit nicely with the overall adaptive control theory framework.
These and our previous comments on the use of synthetically gen
crated data and preposterior analysis present a form1 basis on which learn ing about economic structures and technical response surfaces can proceed. In a more decision oriented context, dual control provides a framework within which exploratory models and policies can be developed. In addit:ion to those already mentioned or implied, there are other areas of possible application for heuristic methods.
One is experimental economics
(Castro and Weingartern [1970]; MacCrimmon and Tota [1909]; Naylor [1972]; Smith
[1962,
1965] ; and Watts
[19691)
.
Most of these studies are closely
connected with the gaming models in h ich learning and heuristic programmiag methods found in i ti ni applicat on.
Few i rops
t
ions of the
tralItlona
nomic theories of individual hchavor hsve been tested in control led
I eco
-55-
experiments; the few tests available refer mostly to the equilibrating pro cess of simple competitive markets (Kigel, et at.
[1975]).
In comparison
with other social sciences where theoretical foundations are not as unified, this is a striking statement.
Applications of systems methods in obtaining
information about how agents learn and operate within various economic sys tems would appear to have substantial potential.
Of course, simulation
methods can be and have been applied advantageously to generate artificial intelligence about the behavior of these economic agents.
However, in the
context of natural resource systems, much remains to be done. Model construction is another activity in which an adaptive framework can be advantageously applied.
Currently, a major limitation associated
with the flexibility of systems analysis and simulation, particularly in the context of explotatory modeling, is the close identity of model and re searcher.
Stochastic control procct.brcs employed in moving from provisienal
to final models of systems can be quite helpful in depersonalizing research results.
In this manner, the sequential modeling approach can aid in making
research results reproducible, and thus verifiable by other investigators. Concerns associatàd with this aspect of systems models and results of simu lations (D.O.D. [1972] and Rausser and Johnson [19751) are likely to provide strong incentives for developing models on the basis of more structured pro cesses. A related development concerns the process of verifying models.
The
discussion of the applications indicates with some notable exceptions (e.g.,
Singh and Day [1971]) that economists have been snnt.awhat lax in corroborat ing models uith sy.tens.
ethods of ‘ccr’plLshin this rrsk ire dcve]oping
rapidly (Rausser und Johnson 119731).
As these athan.es reprcsent an a
SI
-56-
additional means of evaluating comparative models, they should find wider application as systems analysis and simulation become more commonly applied in natural resomce economics research. •
These advances in verification techniques have in large part been made possible by more structured rationalizations for the process of estimating or specializing systems models for particular situations.
In this regard,
the debate surrounding the Forrester [1961] contention that sample and/or past data on the system are not useful in constructing models has been grossly unproductive.
Instead of reaching for an estimation method suffi
ciently general to incorporate the Forrester argument, many researchers have apparently chosen instead to reject statistical and econometric approaches to model construction.
The unfortunate result was, and is, that the asso
ciated models have little generality.
If one cannot establish a correspond
ence of the parameters of a systems model to the underlying system, then the foundations for generalizing the results and verifying the model simply are not present.
In view of these problems, the Mixed (Theil [1971]) and Bayesian
(Zellner [1971]) estimation methods and associated generalizations to the sequential processes involved in model construction (Learner [1974]) represent most promising developments. Applications of the systems models as well are likely to benefit from more highly systematized simulations.
The shopworn and increasingly sus
pect argument that systems analysis presents a method for analyzing problems without a criterion function will soon lose its acceptance.
It is clear
that all models (since they are readily admitted to be purposeful) involve some type of criterion function (Rausser and Frechairn [l974b]).
Recognition
and incorporation or the criterion fanction can prc’vid a basis for condt:crig
-57-
experiments with the systems models which are considerably more informative. In this regard, the works of Zusnian and Amizid [196S] [19701 and Jacohy and Loucks
[1972]
,
Schcchter and Heady
represent examples of methods of model
application which are likely to prevail in future work. The same observations, of course, apply to behavioral and predictive models.
That is, given a criterion for the research exercise, experimental
designs can be advantageously applied to enhance the value of simulated re sults.
Applications of these methods arc likely to produce results of the
type developed by Candler and Cartwright [19711.
Incentives for explicitly
identifying criterion functions are also likely to occur as a result of dif ficulties arising in summarizing simulations.
Without a method of summariz
ing these experiments, the output from model simu’ations can quickly become unmanageable.
However, if summarization is to he useful and accurately rep
resent the outcomes of the experiments, the speci fication of a criterion function is required. Given these comments concerning the structuring f model development and applications, one might counter by suggesting that past applications of the systems approach, in the sense that they were new or novel, were justi fied in proceeding in an unsystematized manner because they were heuristic. Here again, however, there are well-established counter arguments.
In fact,
the major points assceiated with the gathering of artificial intelligence and heuristic modeling (Kuchn and Hanburger [1963] and heier themselves based on systematized search techniques.
[1969]) are
Their imp1icatons for
learning about sys cms through systc-ms anaiysis and sinuiatioa are therefurc’
consistent with th :.a:vhods h ich h. framework with nrce s ng devd onment s
i denti fiud theucL; r ic control
-58-
What are we to infer from these observations on promising developments and their identification with adaptive control processes?
Obviously, they
do not imply that everyone should rush out and purchase a copy of the latest text on stochastic control,
Systems arid simulation applications, although
effectively viewed within the control framework, often present problems which are not currently mathematically tractable.
Even in these instances> the
conceptual basis of control (rather than actual solutions to these adaptive control problems) should be advanced as providing a basis on which systems analysis and simulation can be systematized. Changes resulting from applications of systems and simulation are most encouraging.
They foretell the merger of the theories of individual behavior
with data or empirical evidence and methods of estimation.
It would be un
fortunate not to acknowledge the debt of these advancements to the concepts of systems analysis in the context of natural resource problems.
The ques
tions raised by the development and application of these methods have had a substantial impact in stimulating interest in refining techniques of estima tion and in extending the theory.
At the same time our discussion has hope
fully indicated that systems analysis of natural resource problems as cur rently applied is itself in for some rather substantial alterations.
1
59-
Footnotes 1/
A number of surveys documenting the development of the economic theory
for natural resources and the environment are available; viz., Ciriacy Wantrup [1052], Fisher and Peterson [19761, Mishan [1971), Peterson and Fisher [1977), and Herfindahi and Kneese 2/
[1974).
See, for example, Schaefer [1954, 19571, Smith [1963, 1969), Burt and Cummings
[1969, 19701 and Krutilla [1967).
For formulations emphasiz
ing exploitation of natural resources and technological change, see Rausser [1974, 1975), Rausser and Willis [1976), Dasgupta and Heal [19741, Rosenberg [1973], and Humphrey and Moroney [19751. 3/
The more frequently used definitional frameworks may be found in Chora
fas [1065]. Churchman [1960, 1968], Emery [19691, Orcutt [1960), and more recently. Churchman [1971] and Mihrim [1971]. 4/
Lucid and detailed discussions oE this process arc given by Anderson [1974] and Mihrim [1972].
5/
On a more philosophca1 level, our perspective for the importance of this aspect of economic models has been greatly improved by the develop ment of the notion of a paradigm (Kuhn
6/
Anderson
[1974, p.
25]
points
Out
[1970]).
t is possible to program the ‘ i that T
automatic location of successive experiments
(according to some, steepest
ascent procedure) and the automatic switching to the intensive search which may he accomplished by simply supplementing the last factorial or triangle design into a coaposite or hexagonal second-order design, re spec tjelytt.
-60-
7/
As Starrett [1974, p. 2] recently argued,
,...
one can think of exter
nalities as synonymous with nonexistence of markets, and define an ex ternality to occur whenever the private economy does not have sufficient t incentives to create a potential market.’
The usual definition of an
externality, viz., a decision variable of one economic agent which enters into the production function (or utility function) of some other agent, is far too broad; it defines all commodities in a barter economy as cx ternaliti es. 8/
Artificial intelligence is characterized by Meicr, et al. as
“...
[1969, p.
150)
efficient use of the computer to obtain apparently intelligent
behavior rather than to attempt to reproduce the step-by-step thought process of a human decision-maker”.
It is concerned with computer-
oriented heuristics designed to accomplish such items as search, pattern recognition, and organization planning (Chan Lee
[1974)).
ing and
[1971)
,
Hane [19671, and
In a more sophisticated setting it may also include learn
inductive inference.
I
-61-
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