AN EVALUATION OF JAY FORRESTER'S 'SYSTEMS DYNAMICS' METHODOLOGY

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP80B01495R000600180019-0
• Release Decision: RIPPUB
• Original Classification: K
• Document Page Count: 59
• Document Creation Date: December 19, 2016
• Document Release Date: September 1, 2005
• Sequence Number: 19
• Publication Date: August 1, 1975
• Content Type: MF

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MEMORANDUM FOR: Director of onomic Research
by papers left with Le
I would lik
e some of your
methodologies people to read this and
Ed and me of their views on to q
evaluation of +r e _
F
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1 August 1975
MEMORANDUM FOR: Associate Deputy Director for Intelligence
VIA Director of Economic Research
SUBJECT An Evaluation of Jay Forrester's
"Systems Dynamics" Methodology
1. After having read Forrester's books, listened
to sent three OER analysts to
Ithree-week course on systems dynamics,
and employed an analyst who studied under Dennis Meadows
and Forrester, I conclude that Forrester's method is
absolutely nothing new. Economists have been developing
the same kinds of models for the last twenty-five years.
This view is quite heretical to the devout systems
dynamicists, who for the last decade have preached the
revolutionary nature of their approach, and who still
joust quixotically against the imaginary evils of
economic models.
2. To see why systems dynamics is nothing new,
the simplest approach is to look at the mathematical
structure of Forrester's models. All the models are
essentially systems of difference equations. For example,
suppose that we want to predict international oil prices
and production rates for the next five years. In this
case, the prices are set by oil-producing countries, who
base their decisions on past actions by oil consumers.
The consumers, in turn, take prices as given and adjust
consumption rates. A model of this process--as depicted
by a Forrester snake diagram--could be:
Producers set the oil price
zl for the tth month.
/ f
Time moves on-- Consumers decide
the month t how much oil to
becomes (t+l). buy in the tth
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3. In terms of difference equations, this model
might be written as:
Price(t+l) = a + ~Quantity(t)
Quantity (t) = y + BPrice (t) .
If we know the parameters a, ~, y, and 6, then we can
solve the model for time paths of price and quantity.
As I says, anybody can do it. Moreover,
anyone who has studied economics can recognize the
striking similarity between this model and good old
supply-and-demand analysis.
4. Unfortunately, however, we do not know the
parameters. We do not even know the functional forms
of the relations--on a priori grounds, we could just
as well specify the first equation as Price(t+l) = a{Quantity(t)}~.
5. Depending on the functional forms and the parameters
we assume, a systems dynamics model can yield vastly different
predictions. To pick the "right" model, Forrester's disciples
suggest that we should first make a reasonable guess, and then
test the sensitivity of the model's results to variations in
this guess.
6. This approach neglects an important computational
consideration. In particular, Forrester's models have
dozens of parameters. Should we formulate a relatively small
model with only twenty parameters and twenty plausible values
for each parameter, then our sensitivity analysis would have
to deal with (20)20 possible parameter combinations. This
would make our analysis of oil markets rather complicated,.
because the electricity required for a computer to run
the model would become a major component of oil demand.
7. In summary, the major difficulty in constructing
good predictive models is what it has always been--the
problem of specifying the relations in the models. In
this regard, polemics about the wonders of systems
dynamics are distinctly unhelpful.
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8. Why, then, has Forrester attracted so much
attention? My guess is that he is brilliant in popularizing
difference equations. A difference-equation model, when
written as a set of equations, looks like just another
complicated mass of mathematics. But when the same model
is described by a snake diagram, and when the model's
results are graphed as time paths, then the model becomes
a dramatic analytical edifice. Since this is what people
want, and since Forrester has fervently met the demand, he
is famous.
9. In response to the Forrester cult, I think that
the DDI should take a positive attitude. Those who advocate
systems dynamics models should be told that the Agency certainly
wants to promote sound analytical inferences. To the extent
that the Forrester disciples can justify the relations in
their models, and to the extent the models address important
policy questions, the contributions of systems dynamics will
be most welcome.
10. Nevertheless, Agency analysts should not be forced
to study Forrester's polemics. His books are available for
those who care to read them, and OER personnel will be happy
to answer any technical questions that the books omit.
Chief
Systems Development Group
Office of Economic Research
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28 July 1975
MEMORANDUM FOR THE RECORD
SUBJECT: Summer Computer Simulation Conference
The Summer Computer Simulation Conference was held at
the St. Francis Hotel in San Francisco on 21-23 July.
Approximately 200 of the 450 attendees presented papers at
the conference--about 10 percent of the papers were prepared
by foreign authors.
The theme for the conference was the same as the conference
theme of two years ago: Simulation Credibility. Session
topics at the conference covered a wide range: computer
hardware, software, simulation theory, simulation applications,
in the fields of energy, chemical engineering, medicine,
transportation, etc. Similarly, the spectrum of the papers
presented in the sessions was also broad. In the session
which I chaired, Social and Political Models, the models
dealt with governments as information processing systems,
public budgets, the structure and dynamics of sociological
systems, and secure environments. At the last minute, the
authors of one paper for the Social and Political Model
session were unable to attend. Fortunately,
of the Office of Political Research was able to nresent an
excellent pacer
Because
the Proceedings o the conference were printed prior to the
conference so that complete a ers would be available to the'
attendees for reference, paper will not be published.
Separate copies were giv hose requesting his paper at
he conclusion of the session.
A highlight of the conference was the first (I believe)
major presentation on the status of the MIT National Socio-
Economic Model: The papers were presented in a special
session on Tuesday evening by the members of Forrester's
group at the Sloan School of Management. The papers dealt
with the objectives and the overall status of the project,
the dynamics of economic fluctuations, the production and
work force sectors of the model, and certain issues relating
to the utility and credibility of statistical modeling tech-
niques frequently used, for example, in econometrics. These
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presentations, together with the papers published in the
Proceedings, strongly suggest that the work of Forrester's
group will have a great and lasting effect on all facets of
social and political analysis.
The work is too comprehensive and too complex to be
detailed here, but there are several important facts and
personal judgments which I believe are especially significant:
4
(a) With respect to status, after spending a full
year in carefully working out the broad design of the
model (Phase I), efforts since September 1974 have been
focused on the development of the model's six kinds of
sectors: production sectors which include consumable,
durable goods, soft goods, capital equipment, building
construction, agriculture, natural resources,.energy,
etc.; demographic sectors; household sectors replicating
economic categories--labor, professional, unemployed,
welfare, retired; financial sectors; government sectors;
consumption sectors; and a foreign sector to treat
trade and international monetary flows. The second
phase of the project is nearing completion. All
sectors are operational, and critiques of their behavior
are being solicited from experts in each field--a
massive interdisciplinary approach to model development.
Late in 1975, and thereafter, the model is expected to
produce analyses of national policy issues and alterna-
tives, thereby beginning the fulfillment of its objectives.
(b) Forrester is going to great lengths to use
the model to elicit and exploit expert opinion and
criticism prior to any publication of "results"--no
doubt to preclude, or at least to minimize, the con-
siderable furor that followed the publication of Urban
Dynamics and World Dynamics.
(c) Although focusing on the United States, the
model is generic, i.e., the structure of the model is
designed to be applicable to any region, country, or
combination of countries, by determining and introducing
the parameter coefficients which characterize the area
being modeled.
(d) Concurrent with the development of the model--
it seems to me--Forrester has conducted a companion
effort focused on current methodologies relating to his
work. Reflecting again a facet of the debates following
his publications, i.e., Why is your methodology superior?;
What's wrong with what we're doing?,.?he has begun to
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spell out and document the answers to these questions
in detail. This is especially apparent in the case of
:economics.. Peter Senge of Forrester's group has written
,_a paper which goes to the guts of econometrics--the
statistical methods used in model building--and he
asserts that these assumptions are not valid under
realistic conditions.
It is not unlikely that Forrester's current work will
revolutionize analysis--and, probably, much of-the intelli-
gence process. Regardless of their shortcomings and related
misunderstandings, World Dynamics and Limits to Growth have
clearly changed man's perspectives of the future an time
scales on a global basis. I expect this work to have. an
even greater impact on methodology. The reasons for this
are straightforward: Forrester's methodology readily incor-
porates directly, and exploits, subjective expert judgment
and experience as well as empirical facts and evidence; it
greatly facilitates communication among experts of different
disciplines and between them and the non-experts--the policy
makers and the general public; and he has explicitly identi-
fied fatal flaws in some current analytical methods--especially
econometrics. Importantly, Forrester's method is relatively
simple and straightforward: it is not dominated by mathematics
and statistics practically anyone can "do it." In sum,
although long-suffering and unappreciated, Forrester seems
to be well along in building a methodological nuclear weapon
while concurrently reducing some others which are now widely
used from TNT to something less than dynamite, e.g., demon-
strating that conventional economic methods may not be
merely dismal but, unfortunately, dysfunctional.
From the papers published to date--or Forrester's
presentation at the World Future Society meeting in June, or
Peter Senge's presentation at the Summer Computer Simulation
Conference--my evaluation of the recent work of Forrester's
group may seem overdrawn. Forrester spoke directly to the
implication of Senge's work when I talked privately with him
at the World Future Society meeting. At the conclusion of
the presentations on Tuesday evening, I told Senge that
Forrester had sent me the December 1974 version of his paper
and spelled out my interpretations of its conclusions.
Senge concurred in these conclusions. ?
(a) Attendance at the regular sessions I attended
generally numbered 20 to 30. The attendance at the
Social and Political Model session--..session which had
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not been a part of earlier conferences--varied between
35 and 45.
(b) Dr. Albert Stone with whom I had worked while
at the Applied Physics Laboratory of the Johns Hopkins
University, also attended the conference. He will be
in charge of organizing all sessions on energy for next
year's confererYce which will be held in Washington,
D.C. I agreed to recommend a CIA officer working in
this area to chair one of the energy sessions.
(c) The fact that and I openly
participated as CIA officers appeare to generate no
problems or curiosity whatsoever, quite the contrary.
ST
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VNDERSTANDINC SOCIAL-AM M ECONOMIC CHANGE IN THE UNITED STATES
Jay W. Forrester
Germeshausen Professor
Massachusetts Institute of Technology
1. INTRODUCTION
The MIT System Dynamics Group is currently well ad-
vanced on a national model of social' and economic.behav-
ior.* It is a system dynamics model and so is very dif-
ferent from the more common econometric models. The
present controversies about the economy, uncertainties
about the causes of inflation, and debates about economic
theory all suggest the need for a new approach to eco-
nomic dynamics. We believe there is an excellent chance
that a comprehensive system dynamics model incorporating
the structures that generate economic fluctuations,
growth, and environmental restraints can complement other
approaches and can fill in where other methods of analy-
sis have been unable to answer important questions.
The system dynamics model now nearing completion
should yield substantial new understanding of the major
social and economic pressures confronting the United
States. Within the next few months the model will be far
enough along for us to start examining the forces under-
lying inflation, the nature of the new economic mode that
can simultaneously produce inflation and unemployment,
the impact on standard of living as the United States
buys more energy and resources from abroad, the conse-
quences of various methods of recycling money paid for
oil imports, the effect on exchange rates from foreign
manufacturing by multi-national corporations, and the
economic forces arising to reverse the historical flow of
people from agriculture and manufacturing toward govern-
ment services.
The inadequacy of past precedents and rules of thumb
is becoming evident. Only through modeling will we be
able to develop more promising policies for the future,
and to communicate new insights widely enough to estab-
lish public support for measures necessary to cope with
an increasingly difficult future.
II. SYSTEM DYNAMICS
The economic model now being assembled is a system
dynamics model. As such it differs from more traditional
economic models in structure, sources of input information,
nature of validity testing, and purpose. A brief de-
scription of the system dynamics approach should help in
understanding the model.
System dynamics is a way of combining personal ex-
perience with computer simulation to yield a better
understanding of social systems. The field of system dy-
namics has been under development at MIT and elsewhere
since 1956. Twenty or more books have been published on
subjects ranging from corporate policy to major world
interactions. The principal books from the research pro-
grams have each been adopted as texts in dozens of
universities.
of the background threads on which it builds. In Figure
1, three earlier developments--traditional management of
social systems, feedback theory, and computer simulation--
combine to become system dynamics.. Traditional manage-
ment is the process used to govern social systems
throughout history. Feedback theory or cybernetics is
a body of methods and principles developed during the
last hundred years dealing with how decisions, and the
way they are imbedded in information channels, cause the
dynamic behavior of systems. Computer simulation allows
one to determine the time-varying behavior implicit in
the complex structure of a system.
People start the traditional management process by
observing the world about them, noting the pressures
and reactions of people and groups, and detecting the
linkages and flows of information and influence. From
these observations people form mental images of the
structure of a social system. From the mental images
they attempt to anticipate what will happen next and how
a different policy might make the system behave more
desirably.
. Traditional management processes guide our personal
lives, family affairs, cities, countries, and inter-
national relations. It is the nearly universal approach
to directing human activity. Because it is the basis of
civilization and because it has served well, no quick or
radical break with past tradition is either possible or
desirable.
Traditional management, based on observation and
judgement, has great strengths, but it also has serious
weaknesses. Any new contribution to better management
of social systems must start from the present practices
and move gradually toward improvement. Any better
method of decision-making must build without discon-
tinuity on the strengths of traditional management while
compensating for the weaknesses.
The greatest strength of traditional management
comes from the wealth of information available from the
separate observations and experiences of people. In
the mental stores of knowledge are probably a thousand
or million times more information than has been con-
verted to written from in libraries. In turn, written-
descriptions cover a thousand or million times the
scope and richness of information that is available in
measered and numerical form. If we are to improve on
social decisions, we must be able to build on the most
comprehensive information base available-the observa-
tions, knowledge, and judgement stored in people's
heads. System dynamics uses that descriptive informa-
tion along with any available written and numerical
information.
But traditional management has several serious
weaknesses. System dynamics helps to alleviate those
weaknesses.
A. Background of System Dynamics
System dynamics in perhaps best described in terms
*The National Modeling project is being supported by the Rockefeller Brothers Fund.
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Trod rhonaI
management
of social systerp's, .
Feedback theory
or cybernetics.
Computer
armutation
Dynamic behavior
Mode I and improvement
of policies
Figure 1. Background of system dynamics.
from the very wealth of information that is the greatest.
strength. In fact, we have too much information. We
are flooded and overwhelmed with information. The tradi-
tional processes contain no general principles or organ-
ized philosophy for picking the relevant from the extra-
neous information. As indicated in Figure 1, principles
drawn from feedback theory assist in choosing from the
excess of information that which is relevant to the be-
havior modes of interest.
The second weakness of traditional management arises
from lack of organizing principles for the structuring of
information. Even if the first weakness is overcome and
the relevant information and relationships are chosen, no
guidelines exist for organizing the chosen assumptions
into a structure that explains the observed system be-
havior. Again, feedback theory offers principles [8)
for simplifying and organizing the structure of a system.
But even if information is effectively selected and
usefully organized into a relevant model, traditional
management encounters a third weakness. Even when as-
sumptions are explicitly stated, the human mind is not
well-adapted to determining the future time-varying con-
sequences of those assumptions. Different people, even
when they accept the same assumptions and structure,
often draw contrary conclusions. A consensus is hard to
reach. and even a majority opinion may be incorrect. As
suggested in Figure 1, computer simulation can be used
to determine, without doubt, the future dynamic impli-
cations of a specific set of assumptions.
`'Tosummarize, system dynamics starts from the prac-
tical world of normal economic and political management.
It does not begin with abstract theory nor is it re-
stricted to the limited information available in numerical
form. Instead it uses the descriptive knowledge of the
operating arena about structure, along with available
experience about the decision-making. Such inputs are
augmented where possible by written description, theory,
and numerical data. Feedback theory is used as a guide
for selecting and filtering information to yield the
structure and numerical values for a computer simulation
model. Because the resulting models are too complex for
either intuitive or mathematical solution, a computer
simulates, or plays the roles, of the many participants
in the system to determine how they interact with one
another to produce changing patterns of behavior.
_. Necessity for Models
Models are not new in social decision making. Sys-
tem dynamics does not for the first time introduce
models into the social and political process. Mod.1a
have always been the basis for the traditional manase-
ment methods.
Every decision we make is based on a model. On.
does not have a family, city, or nation in his head. t,
has only images, relationships, and abstractions fr.r!
real life. These perceptions are models in the sass
sense that the word is used in system dynamics. one
uses observation to form a mental image, or model. :tt.
mental model becomes the basis for decisions.
System dynamics does not impose models but I. a
way of improving on the models that would otherwise be
used to manage human affairs. The system dynamics m'.:s:
is more explicit than a mental model, so it can be c.e,-
municated with less ambiguity. A system dynamics ca.:?:
Is more carefully structured in accordance with dycea:,
principles, so it better relates underlying assumpti-e?
to system behavior. A system dynamics model can be
simulated on a computer, so, unlike a mental model, its
behavioral implications can be determined precisely.
C. Comparing System Dynamics with Econometrics
System dynamics is a departure from conventional
methodology in economic modeling. Most major economic
models have used econometric methods to convert histor-
ical numerical time-series data into parameters for all
assumed structure of equations. But such methods his.
failed to answer pressing questions about fundamental
behavior arising from social, economic, and environ-
mental interactions. The current national issues are
so critical that a new approach should be tried. C.10-
pared to an econometric model, a system dynamics model:
a. makes greater use of descriptive information
and managerial and political experience
b. incorporates a broader range of.variables and
encompasses the many relevant disciplines
outside of economics
c. uses numerical data from real life in a differ-
ent way--in model construction to complement
descriptive information, in validation to c,"*'
pare with corresponding output data from the
model
d. generates social and economic fluctuations and
growth from the internal feedback structure
without using exogenous variables to drive
change
a. Includes important social and psychological
variables for which statistical data are not
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available.
f. explains how "structural changes" occut as the
economy moves into new modes of behavior that
are not represented in past time-series data
g. facilitates incorporating the wide range of non-
linear structures that generate so much of
observed real-world behavior
b. emphasizes the conservation of flows by including
the buffer stocks that decouple the instantaneous
fl rates F
ow
But bow closely must the demands of theory be ap-
proximated? The answer cannot be found in the real-life
setting but can be determined in controlled laboratory
experiments. A dyna..c, feedback model can be defined
without exo-
te
,
as the "real" system and used to genera
genous driving variables, time-series data comparable to
that collected in real situations. The data-generation
model stands in the place of the real system. Separate-
ly, an estimation model is used by a statistical analyst
as an approximation to the "real" systen as is done in
the usual data-analysis procedures. All conditions of
the process are completely controllable. The statisti-
calanalyst can he all"wad to kn^' p? ^'-ch or as little
about the structure of the "real" system as desired.
The random noise processes within the "real" system can
be controlled. The interval between data samples can be
independent of the dynamic processes within the "real"
system. Controllable errors can be inserted in the data
collected from the "real" system. The degree of corre-
spondence between the structure of the "real" system
and the structure of the estimation model can be con-
trolled. And finally, perfect knowledge is available
about the structure and parameters of the "real" system
to permit a definitive evaluation of the parameters ob-
tained by the statistical methods.
Such comprehensive examination of the practical as-
pects of statistical model-building has recently been
started. The first tests, done on single-equation least
squares regression analysis, reveal the consequences of
various deviations from the theoretical assumptions
underlying the standard procedures. It is beginning to
appear [9] that least squares regression, which is pro-
bably the statistical method most often used by social
scientists, is highly sensitive to surprisingly small
departures from the idealized theoretical foundations. In
fact, the statistical methods break down and become mis-
leading with such minor departures from perfection that
meeting the theoretical requirements closely enough
seems inconceivable.
The laboratory tests indicate that the generalized
least squares data analysis can give not only major
n
di
i. distinguishes more sharply between real variables,
their money value, and information about them to
capture the dynamic interactions between the
real, money, and information aspects of a system
J. encourages construction of a deeper substructure
of feedback loops to represent causal mechanisms
underlying macroeconomic behavior
k. organizes structure so that each parameter has
independent real-life meaning in the operating
world and can be individually drawn from and
checked against descriptive and quantitative
information available at the place in the real
system to which the parameter applies
1. serves as a more effective communication medium
for resolving disagreements because of the way
both model structure and parameters correspond
with descriptive knowledge in the operating
world
M. places more emphasis on the importance of
Internal structure
n. focuses more on understanding the reasons r
observed behavior and on developing policies to
produce better behavior, and focuses less on
prediction
o. combines over a greater time span the short-term
with long-range human objectives
p. permits a wider diversity of contact between the
model and the real world to make validation more
persuasive.
D. Avoidin the Practical Difficulties with Statistical
Models
A system dynamics model can circumvent the major
practical shortcomings that-keep econometric methods
from deducing correct parameter values and from correctly
-evaluating the validity of hypothesized structures.
Dissatisfaction with econometric models is widely re-
flected in the economics literature. Although failures
have usually been attributed to inadequate data, a more
fundamental reason is emerging for the deficiencies in
econometric models.
The statistical methodologies are based on precise
theoretical foundations regarding correspondence between
the hypothesized model structure and the structure of
the real system, the nature of random disturbances in
the real system, tae characteristics of auto and cross
ollected
f
e
c
correlation, the frequency of sampling o
data, and the absence of measurement errors in the data. from direct observation of processes in the actual social
As recognized by almost everyone, none of the underlying system. Unlike econometric models, system dynamics
theoretical requirements are fully met, so the practical . models are structured to facilitate parameterization by
application of econometrics rests on the assumption that direct observation of the real-life decision-making pro-
the theoretical requirements are approached sufficiently ceases. In a system dynamics model every parameter can
closely for the methods to be applicable. cuhave ssednanddevaluatedrinlterms Ireat dexis-
As long as econometric methods are applied only in tence. Those familiar with the structure and policies
real situations, no final test of methodological accuracy of the particular part of an actual system have the
is possible because the true values of the real system necessary information to evaluate the reasonableness of a
parameters are not available for comparison with para- parameter value. And reasonable values are usually suf-
mater values that have been deduced from statistical ficient because behavior of a typical complex social
analysis. In ordinary practice the estimates of validity structure is surprisingly insensitive to most parameter
are entirely internal to the statistical process itself, values. [1, pp. 57-59, 105, 118-119.]
so the estimate of validity also rests on the assumption.
that underlying theoretical requirements are adequately
pet. ?
g
errors in the estimates of parameters but also mis ea
indications from the internal validity measures. Accu-
rate parameters can be obtained in a correct structure
for the estimation model along with validity measures
that suggest low confidence; depending on such results
of the analysis would lead one to discard correct para-
meters and structure. Or, at other times, inaccurate
parameters can be obtained in a correct structure of the
estimation model along with validity measures that sug-
gest low confidence; the likely action based on the low
validity measure would be to discard the correct struc-
ture in the estimation model.
These laboratory experiments indicate that statis-
tically-derived parameters are likely to be further in
rror than the estimates made for system dynamics models
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III. DYNAMICS TO BE REPRESENTED
The new model of the economy addredees?'a wide range
of dynamic behavior. The structure should be detailed
enough to generate most of the major characteristics ob-
served in the real economic system. Dynamic behavior
can be described in terms of periodicities, modes, and
time horizon. These characteristics are discussed below.
The business cycle of some three to seven years
duration probably arises from interaction between tnv.e.
tories and employment. More commonly, the business cy_..
has been attributed to capital investment, but the p ; is.
ning time and life of capital are long enough to rusn'6t
that the primary contribution of capital investr.cnt I. ,,
a longer fluctuation in the economy. By reaching 1,..-,
to the fine structure of employment, inventory manA,e.,.,t
and materials procurement, the model should deal c+,r.
rectly with the business cycle [10].
One might separate into j.mdividual models the dif- In the intermediate range of behavior, some evidrnce
ferent rapidities of response in a system. Each model suggests a cycle (the Kondratyev wave) in the econeey of
would be designed to examine a particular kind of behav-- some fifty years duration. The existence of such a I_,n;
for. On the other hand, in a national socioeconomic wave is important to explore. If it exists, its last
system the wide range of inherent periodicities may collapse was into the depression of the 1930's, and its
overlap and influence one another. Oscillatory modes of next could be imminent. The long wave may have a more
similar duration might pull together and entrain one powerful. effect than the business cycle.
another into a single dynamic behavior. Or they might
remain separate but enhance one another's effect. Be- At the slowest end of the time spectrum is the life
cause so little is known about the diversity of such cycle of economic development. For the first time, it.
interactions, the present model combines a wide range of industrialized societies seem to be moving into a new
dynamic phenomena into one structure. phase of the life cycle of growth. If so, the United
States is now at a point of departure from past trends
The model will simultaneously be able to create a and expectations such as occurs only once in the history
wide span of time responses--from the business cycle on of each civilization. As shown in Figure 2, the economy
the short end, through intermediate interest-rate-capital- now appears to be in.the "transition stage" between
investment cycles, to the once-in-history transition from growth and some form of future equilibrium in population
growth to equilibrium. To do so will require a structure and industrial activity. In the past, we have experi-
containing the short time constants associated with in- enced exponential growth, with a doubling of economic
ventories, backlogs, and bank balances. The model also output every twenty or thirty years. Such growth cannot
represents the slower processes associated with accumu- go on forever. There must be a leveling out or a peaking
lation of buildings and machinery, and the movement of and decline. The debates are about when and how the
people. At the long end of the time spectrum, the model past kind of growth will end, rather than about whether
should contain population growth, land occupancy, and or not it eventually must end.
resource depletion.
32
16
-Growth
Production
1890 1910 '30 '50 1970 '90 2010 2030
4
2L
?
'Figure 2. Life cycle of economic growth.
.. 12t~ as v' t.. .,. .. r..
a I.
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The transition period is about half-way up'tb1 life-
cycle curve of economic growth and occurs some two doub-
ling times before the economy reaches a peak. Doubling
times have been some twenty or thirty years long. At
present, about fifty years before we can expect a peak-
ing of population and economic activity, is the time
when social and economic forces are pushing us out of
the old growth mode.
I believe we are in the transition stage. The.tran-
sition stage is consistent with the social, environmental,
and inflationary forces that are developing. A model
that is to cope with today's issues must incorporate
not only the recurring processes of past business-cycles,
but also the transition process triggered as an economy
and its population begin to exploit fully the available
energy, resources, agricultural lands, and water.
The time of greatest social and economic stress
occurs during the transition stage, not during equilib-
rium. When equilibrium has been reached, the nature of
$he new mode of social and economic behavior will be
understood and accepted; But in the transition stage,
sufficiently great forces arise to overcome the old en-
gines of growth. Laws, attitudes, management methods,
traditions, values, expectations, and religions must all
change. The.eransition?stage is the time of turbulence
as the system moves out of the growth mode.
A socio-economic model to deal with today's ques-
tions should encompass the short-term dynamics of the
business cycle in concert with the structures that may
produce a 50-year long wave and against the background
of the life cycle of economic development. For the first
time we may face the triple coincidence of a business
downturn, a long-wave collapse, and the pressures of the
transition region. The three could combine to depress
economic activity and the standard of living.
System modes can be described in terms of the asso-
ciated restraints. The typical economic system is pro-
bably unstable in a free mid-range region where re-
?straints are not dominating behavior. In such a re-
.straint-free region there will be a strong tendency for
the economic system to move toward one of the possible
restraints. If this is correct, shifting modes of eco-
nomic behavior can be described in terms of the successive
restraints that dominate behavior.
At the beginning of industrialization when there was
ample land and an excess of labor, the restraint was in-
sufficient capital equipment. The whole philosophy of
capitalism arose from the capital shortage that deter-
mined the pace of economic development. But after World
War II the United States economy moved out of the mode'
dominated by a shortage of capital.
In the 1950's and 1960's the United States economic
system has been characterized more by a shortage of man-
power than by a shortage of capital. This has been indi-
cated by chronic shortage of labor and by use of much of
the capital plant only 8 hours a day instead of 24. In
many businesses capital has been in sufficient supply
that it is scheduled for the convenience of people. Be-
cause labor has become the principal restraint, labor de-
mands set the style and pace of the economic system.
Now the United States is moving once again into a
aev'mode characterized by shifting restraints. The mode
of labor shortage is giving way to the mode of environ-
mental shortage. Environmental shortage exists in terms
of space, agricultural land, pollution-dissipation capa-
city, resources, and energy.
The model should move through these various modes
not in response to exogenous driving assumptions, but
under the progression of its own internally generated
social and economic forces. In effect, the model em-
bodies a theory of economic development that can be
tested by seeing if it will generate the modes of behav-
ior that have been observed.
If the model is successful in making the transitions
between social and economic.modes, it should help reveal
the nature of the transitions, their causes, the forces
to be expected during any specific change, and the poli-
cies that would establish and sustain a desired mode.
C. Time Horizon
To generate the wide range of periodicities and
modes, the model must be conceived in terms of a long
time horizon. The model should create appropriate growth
and fluctuation from the year 1800 to 2100. The model
should generate behavior typical of the past as a base
frem-which to anticipate the future. Generally speaking,
forces and structures visible at any point in time domi-
nate a very long way into the future. If the fundamental
nature of the present system is carefully examined, most
essential dynamic mechanisms for the next several decades
should be detectable.
A model with a 300-year time horizon imposes special
demands on its parameters, variables, and structure. Any
constant in the model must be constant for 300 years and
must transcend the entire life cycle from early indus-
trial growth through all the traumatic changes of the
present and near future and into a mode of equilibrium
behavior very different from the past. Therefore, para-
meters must be extremely fundamental. They become de-
scriptions of human psychology at a stable.level that
does not shift in response to the immediate political and
economic conditions. Any social attitudes, ethical prin-
ciples, or human preferences that themselves evolve from
the surrounding economic and geographic circumstances
must be cast as variables responsive to the socio-eco-
nomic pressures. The model must be anchored on concepts
so fundamental that they represent human psychology and
descriptions of nature that are not subject to change by
the forces the model itself is exploring. Concepts that
are more fleeting must be formulated as variables and
generated by the forces from which they arise.
IV. SOCIAL AND ECONOMIC ISSUES
A model should be constructed for specific purposes.
The purposes come first and shape the design of the
model. The purposes for this socio-economic model can be
described in terms of the issues to be explored.
A. Inflation
The model is planned for examining the forces under-
lying inflation. Today's inflation is a much deeper
issue than revealed by the public press or by explana-
tions in the economics literature. It is much more than
a question of inflation versus unemployment.
Present inflation arises from major imbalances in
the economy. Some two-thirds of employment is outside of
agriculture and direct production. This constitutes a
very high overhead.in government, education, and the ser-
vice industry. Two-thirds of the working population in
overhead is probably too great for the economy as we
move out of uninhibited economic growth into a period
when production is progressively more limited by environ-
mental restraint while, at the same time, population con-
tinues to rise. Much of the inflationary pressure comes
from governmental efforts to sustain a rising standard of
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living when real output per capita is running into in-
herent barriers.
The efforts to hide, by monetary and fiscal means,
the fundamental changes now occuring in the industrial-
ized economies are driving inflation. Changing social
attitudes,. greater complexity arising from crowding. and
'increasing capital investment required as space and re-
sources become overcommitted are all interlocked in the
inflation syndrome.
Actions taken to counter inflation, like escalator
clauses in contracts and "indexinJ" of future payments
to compensate for inflation, may accelerate inflation.
Such changes in the legal structure of the economy
should be studied in a realistic model before being put
Into practice.
3. Recession, Depression, and Unemployment
Most important in the near future, the model should
replicate changes now occurring in the economy. By dup-
licating the gathering economic stresses, the model
should be an effective vehicle for better understanding
the causes and cures for recession coupled with inflation
and a vulnerable credit and banking system.
Current national economic actions are those that
might be appropriate to a normal business-cycle reces-
sion. But the forthcoming changes may be far more than
a recession. If we are at the peak and entering the
steep decline of a 50-year capital-investment cycle, the
cause is over-investment in office buildings, automobiles,
and many kinds of production facilities. Under such cir-
cumstances, national policy to sustain investment may
simply delay a needed realignment within the economy.
To the extent that the final slowing of long-term
economic growth is behind the present economic stresses,
the fundamental issues are more demographic and environ-
Mental in nature than economic, and solutions call for
redirecting the national focus of-attention. A substan-
tial percentage of the work force is devoted to creating
-growth and to coping with the strains arising from
growth. When growth slows in the late part of the eco-
nomic life cycle, substantial unemployment will develop
from jobs that need no longer be filled. The day of
reckoning can be delayed but not escaped. The further
ahead we recognize changes imposed by the life-cycle
of economic growth and work toward an orderly evolution
of the socio-economic system, the less traumatic will be,
the realignments. Because of the extreme complexity of
interactions between social, financial, technological,
and demographic forces, only a comprehensive model will
give access to the behavior we need to understand.
The dynamics of the Great Depression of the 1930's
should be examined in search of a better understanding of
causes. Was it merely from governmental mismanagement of
the financial system? Was it random bad luck? Was World
War I significant? Was it the collapse phase of a
50-year cycle? Did it arise as a consequence of the
Major migration from: farm to factory? Can it recur?
C. Wage and Price Controls
The model contains separate price and wage genera-
tion in each production sector. By suppressing changes
in one or more of these, the effect of price and wage
controls can be examined. Prices and delivery delays
(availability) influence flows in the model, so the model
should realistically respond to controls and should show
how controls might transform price pressures into other
social and economic pressures.
D. Nature ofEtonomic Growth
Th. model, by linking population, environment,
knowledge generation, and technological contribution rs
productivity, should provide insights into the nature
and future of economic growth. The world has been pur-
suing economic growth with success in some countries .n4
lack of success in others. The model can be used mine reasons for past growth and to examine whether or
not the gains of the past can be sustained.
Economic growth is inherently a transient process.
It cannot continue forever. But where does it lead?
Will the higher standard of living be.sustained in the
future or fall back? The answer depends on how popula-
tion, technology, and nature interrelate. The standard
of living rises when production grows faster than popu-
lation. But as limitations of energy, resources and
space slow the growth of production, growth in population
may be slowed more or less quickly with a consequent re-
tention or loss of the standard of living achieved by
past economic growth.
The end of economic growth in the equilibrium stage
of Figure.2 can take many forms. If population rises
faster than production in the late stages of growth,
standard of living peaks in the transition stage and then
declines. The end point of economic growth can move
toward conditions found in India. People have strived
mightily to initiate a US-type economic growth in India
without success. The reason may be that India has al-
ready arrived at the end of the economic growth life-cycle
--a condition in which population can exceed the capacity
of the country's land and resources.
Economic growth in the United States (and, based on
external resources and markets, also for Japan and West-
ern Europe) has been a very special case. Overlooking
the way the American Indian was evicted, the United
States was a huge empty country of rich agricultural land
and plentiful resources and energy. Economic growth has
consisted of filling that land with population while
using the bounty of nature. But such a growth process
is transient. It cannot continue. As growth falters,
the nature of the socio-economic system changes. To
what? Many choices lie in the future. Now is late but
not too late to choose.- But we must first have a way to
examine the alternatives and the policies leading thereto.
As an economy moves through its growth life cycle,
the role of agriculture changes. At the beginning the
economy is rural. As capital accumulates and labor be-
comes scarce, and if energy is ample, agriculture becomes
capital intensive. The productivity per worker in the
field increases but not necessarily the output per unit
of energy input. American. agriculture is actually a low-
efficiency converter of petroleum calories into food
calories, a useful process when energy is plentiful but
less effective when energy shortages develop. Toward
the end of economic growthas labor becomes excessive and
energy and land become scarce, a transfer of labor back
to agriculture is probably necessary. Such a reversal of
labor migration should be examined because it affects
government policies on housing, transportation, welfare,
and unemployment compensation.
F. Population and Standard of Living
As the capacity of a country becomes fully committed.
a tradeoff must exist between population and the standard
of living. The higher the population the lower will be
the standard of living. The compromise faces each coun-
try. Whether or not the issue is recognized will mold
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the future character of the society. Populatioh'versus
standard of living does not concern underdeveloped
countries alone. Population density of Massachusetts is
one and a half times the population density of India.
Internal capacity of Massachusetts to support that pop-
ulation is probably little better than India's. Indus-
trialized countries have been buying low-cost resources
and selling high-priced manufactured exports.
the balance shifts and resources become scarce while the
capability to manufacture spreads,..l he status of the
have and have not nations begins to converge. As every
aspect of the world's capacity becomes more fully com-
mitted, each country will begin to face life within the-
scope of its own land and resources. Major internal re-
alignments will be occurring. The economic mode of the
future can be substantially different from the past. A
eational socio-economic model, if comprehensive enough,
should help anticipate the-actions necessary in the
readjustment period.
G. Education and Economic Change
J. Balance of Payments
As the prices of energy and resources rise relative
to manufactured goods, the balance of payments deficit
alters exchange rates and drives down the internal stan-
dard of living. Governmental policies affecting trader
can have different long-term and short-term effects.
Policies to alleviate immediate pressures can accentuate
future problems. The trade-offs need to be evaluated in
terms of the internal and external economic consequences.
A dynamic economic model with an external sector from
which to buy resources and sell goods should allow the
study of national coupling to the international economy.
The structure of the socio-economic model is in-
tended to be general and to apply to any country having
agriculture, consumption, manufacturing, and money. By
concentrating first on the United States economy, while
keeping in mind the desire for generality, the structure
should be rich enough in detail to be a good represen-
tation of not only other industrial economies but also
the underdeveloped and developing countries. Fitting
the model to a particular country would merely require
selection of suitable parameters and initial conditions.
However, all present work is in terms of the United
States.
A. Overview
The model will treat all major aspects of the socio-
economic system as internal variables to be generated by
the interplay of mutual influences within the model
structure. The model will contain production sectors,
labor and professional mobility between sectors, a demo-
graphic sector with births and deaths and with subdivi-
sion into age categories, commercial banking to make
short-term loans and generate credit, savings institu-
tions to accept saving and to make long-term loans, a
cre-
monetary authority with its government fiscal money and i operations,
dit, government services, g g
consumption sectors, and a foreign sector for trade and
international monetary flows.
A generalized production sector is being created
with a structure comprehensive enough that it can be
used, with selection of suitable parameters, for each of
some fourteen or more producing sectors in the economy.
Each sector will reach down in detail to some eleven factors
of production. ordering, and inventories for each factor
K. Fiscal and Monetary Policy
Economic and political debate has centered on poli-
cies for managing the economy, enhancing economic growth,
and reducing unemployment. But have the policies been
effective? The reduced amplitude of business cycles in
the post-war years is often cited as evidence for effec-
tiveness of such policies. But the suppressed business
cycle may instead reflect other causes--the effect of
governmental transfer paytrients, phase of a of the economy, or the rising p e
wave caused by labor shifts and the dynamics of capital
accumulation. Past policies may have contributed more to
inflation than to reducing employment or stabilizing
the economy.
Reviewing past policies is important, lest incorrect
interpretations lead to misguided future action. With
internal monetary and fiscal sectors and.with taxation,
debt management and government expenditures, the new
economic model should offer a basis for resolving de-
bates over Keynesian versus monetarist proposals for
government intervention in the economy, and how each is
related to growth, stability, and inflation.
V. STRUCTURE OF THE MODEL
Education is a form of capital investment. Educa-
tion increases skill, production output, and human sat-
isfaction. But much of education has been used to fill
the inventory of skills; with the inventory filled, only
replacement is needed. The educational system, like
several other parts of the service sector, shifts from
being inadequate to being over-extended as the economy
passes the steepest part of its growth. Evidence of ex-
cess capacity in higher education is appearing. overn-
pressures
ental al action to withstand developing
sustain historical trends may only. lead to more drastic
readjustments later. By interrelating consumption de-
mands, productivity, technology, and balance of skills,
the model should generate the rising and falling balances
between sectors of the economy.
H. Capital Utilization
During growth, production is primarily dependent on
capital and labor. As long as land and energy are avail-
able, the standard of living rises as the capital-to-labor
ratio increases. But resources, energy, and environmental
capacity are consumed. In time, growth impinges on
ural restraints. When the environment is fully committed,
total production is limited by the capacity of nature and
the standard of living is determined by the nature-to-
population ratio. Under the latter circumstances, the
capital-to-labor ratio becomes irrelevant to total pro-
duction, which is set by environmental limits. Instead,
the capital-to-labor ratio becomes a social issue. Cap-
ital intensive production with few people working can be
combined with income redistribution for supporting others.
Or, labor intensive production can be chosen in response
to a social decision giving each person a right to a job.
Such issues need clarification.
1. Taxes
The consequences of collecting taxes from different
points in the economy should be examined. Congress and
state legislatures endlessly debate the merits and equity
of who to tax and how. What are the relative advantages
of property tax, personal income tax, corporate income
tax, sales tax, or value-added tax. Such questions may
have only a short-term significance. In the longer run,
prices and wages can readjust so that money flows to the
point from which it is extracted. The structure of the
economy suggests that the total tax levied may be far
more important than the method. If so, types of taxation
may have little leverage for inducing social change, in
spite of the rhetoric addressed to taxation issues. A
Comprehensive model incorporating various channels of
taxation and containing the processes of price and wage
setting should permit evaluation of tax policies.
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of production, marginal productivities for each factor,
balance sheet and profit and loss statement, output in-
ventories, delivery delay computation, production-rate
planning, price setting expectations, and borrowing.
The model is being formulated for tfie new DYNAMO III
compiler, which handles arrays. of equations and makes
especially easy the replication of the production sector
and its subparts. For example, an equation in the
ordering function. need be written only once with array
subscripts to identify the ordering, functions for each
factor and sector. P
When fully developed, the model will contain some
2000 level variables (referred to variously as integra-
tions, state variables, stocks, or accumulations). This
compares with 22 level variables in the Urban Dynamics
model and 5 in World Dynamics. The total number of de-
fined variables are about six times the number of level
variables.
By reaching from national monetary and fiscal
policy down to ordering and accounting details within an
individual production sector, the model will bridge be-
tween the concepts of macro-structure and micro-structure
in the economic system. We believe that the major modes
of the economy arise from such a depth of structure and
that highly realistic and informative behavior should
emerge front such a degree of disaggregation.
B. Standard Production Sector
A standard production sector will be replicated to
form a major part of the model. By choosing suitable
parameter values, the standard sector can be used for
consumer durable goods, consumer soft goods, capital
equipment, building construction, agriculture, resources,
energy, services, transportation, secondary manufacturing,
knowledge generation, self-provided family services, mil-
itary operations, and government service. Such general-
ity focuses attention on the fundamental nature of produc-
tion of goods and services and simplifies both con-
struction and explanation of the model.
Within each production sector are inventories of
some eleven factors of production-capital, labor,
professionals, knowledge, energy, services, buildings,
land, transportation, and two kinds of materials. In
adiition, production is affected by length of work week
for labor, length of work week for capital, and the
content of each of the two kinds of material in the
product.
For each factor of production, an ordering function
will create an order backlog for the factor in response
to desired production rate, desired factor intensity,
marginal productivity of the factor, price of the factor,
price of the product, growth expectations, product inven-
tory and backlog, profitability, interest rate, financial
pressures, and delivery delay of the factor. In terms
of dynamic behavior, the ordering function will be far
more influential than the production function, yet, in
the economics literature, attention has been in the re-
verse priority.
The structure of a standard production sector is
essentially the structure of a single firm in the economy
with parameters and nonlinear relationships chosen to
reflect the broader distributions of responses resulting
from aggregating together the many firms within a sector.
As with a firm, the sector will have an accounting sec-
tion that pays for each factor of production, generates
accounts receivable and payable, maintains balance sheet
variables, computes profitability, saves, and borrows
money. The structure'should generate the full range of
behavior that arises from interactions between the real
and the money and information variables. By carrying
the model to such detail, it should communicate directly
with the real system where a wealth of information is
available for establishing the needed parameter-values.
A sector will generate product price in accordance
with conditions within the sector and between the sector
and its customers. For testing price and wage controls,
coefficients are available to inhibit price changes. The
sector will distribute output among its customer sectors.
Market clearing, or the balance between supply and
demand, will be struck not by price alone but also on
the basis of delivery delay reflecting availability,
rationing, and allocation.
C. Labor and Professional Mobility
People in the production sectors are divided into
two categories--labor and professional. For each cate-
gory a mobility network defines the channels of movement
between sectors in response to differentials in wages,
abailability, and need. A mobility network has a star
shape with each point ending at a production sector and
terminated in the level representing the number of people
working in the sector. At the center of the star is a
general unemployment pool,.which is the central communi-
cation node between sectors. Between the central pool
and each sector is a "captive" unemployment level of
those people who are unemployed but who still consider
themselves a part of the sector. They are the people
searching for better work within their sector or who are
on temporary layoff but expecting to be rehired. In a
rising demand for more labor, those in the captive level
can be rehired quickly but longer time constants are
associated with drawing people from other sectors by way
of the general unemployment pool.
The demographic sector generates population in the
model by controlling the flows of births, deaths, immi-
gration, and aging. Age categories divide people into
their different roles in the economy from childhood
through retirement. The demographic sector divides peo-
ple between the labor and professional streams in re-
sponse to wages, salaries, demands of the productive
sectors, capacity of the educational system, and family
background. Workforce participation determines the frac-
tion of the population working in response to historical
tradition, demand for labor, and standard of living.
3. Household Sectors
The household sectors are replicated by economic
category--labor, professional, unemployed, retired, and
welfare. Each household sector receives incomes, saves,
borrows, purchases a variety of goods and services, and
holds assets. Consumption demands respond to price,
availability of inputs, and the marginal utilities of
various goods and services at different levels of income.
The financial sector is divided into three parts--
commercial banking, savings institutions, and the mone-
tary authority. The financial sector determines interest
rates on savings and bonds. buys and sells bonds, makes
long-term and short-term loans, and creates intangible
variables like confidence in the banking system.
The commercial banking system receives deposits,
buys and sells bonds, extends loans to households and
businesses, and generates short-term interest races. In
doing so it manages reserves in response to demands of
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the monetary authority, and acts in response..to,discount
rate, expected return on investment portfolio, demand
for loans, and liquidity needs.
The savings institution receives savings, extends
long-term loans to households and businesses, generates
long-term interest rates, buys and sells bonds, and
borrows short-term from the banking system. The savings
institution balances money, bonds, deposits, and loans.
It allocates loans between businesses and households,
and it monitors the debt levels and d borrowing capability
of each business and household sector.
The monetary authority controls discount rate, open
market bond transactions, and required reserve ratios.
In doing so it responds to such variables as owned and
borrowed reserves of the bank, demand deposits, infla-
tion rate,?unemployment, and interest rates.
VI. STATUS, SCHEDULE, PROCEDURE
Phase One of the project has been almost entirely
devoted to completing a preliminary formulation of the
model that can become the basis for discussion and im-
provement. Such a preliminary model can be a powerful
communication medium for eliciting inputs from experts.
Because the model clearly reveals the assumptions made
in the preliminary'cormulation, those with different or
additional perceptions of the actual system can immedi-
ately identify errors and omissions. Preliminary model
formulation is'now nearly complete.. At the present time
(March 1975) assembly is.under way and should be com-
Phase Two from'September 1974 through Aug!st 1975
includes a search for advisors and participants from
whom to solicit suggestions for reformulation and improve-
ments. The structure of the model and the nature of the
DYNAMO III compiler permit very easy modification of the
model. Because the model is so much better for communi-
cation purposes after a preliminary sec of equations are
operating,.the most efficient time to use outside advice,
criticism, and suggestions is after the preliminary model
is usable. Individuals and organizations are now being
identified with whom to interact to improve the, model and
to begin interpreting its implications.
Phase Three will extend through the last third of
1975 and possibly for a decade beyond. During Phase
Three a widening circle of participants should become in-
volved in a progression of discussions, model modifica-
tions, and publications on structure, behavior, and impli-
cations. As sufficient confidence in the model develops,
the national issues to which it is addressed will be
explored.
1. Forrester, Jay W. Industrial Dynamics, MIT Press,
Cambridge, Mass.,. 1961.
7. Forrester, Nathan B. The Life Cycle of Economic
Development, Wright-Allen Press, Inc., Cambridge,
Mass., 1973.
2. Forrester, Jay W. Urban Dynamics, MIT Press,
Cambridge, Mass., 1969.
3. Forrester, Jay W. World Dynamics, Wright-Allen
Press, Inc., Cambridge, Mass., 1971.
4. Oltmans, Willem L., On Growth, G. P. Putnam's Sons,
New York, 1974.
5. Forrester, Jay W., Gilbert W. Low, and Nathaniel J.
Mass. "The Debate on World Dynamics: A Response to
Nordhaus," Policy Sciences, vol. 5, June, 1974.
6. Forrester, Jay W. "Educational Implications of Re-
sponses to System Dynamics Models," Management Sci-
8. Forrester, Jay W. Principles of Systems, Wright-
Allen Press, Inc., Cambridge, Mass., 1971.
9. Senge, Peter M. "An Evaluation of Generalized
Least Squares Estimation," System Dynamics Work-
ing Paper D-1944-6, December 6, 1974, Alfred P.
Sloan School of Management. Massachusetts Insti-
tute of Technology.
10. Mass, Nathaniel J. Economic Cycles: An Analysis
of Underlying Causes, Wright-Allen Press, Inc.,
Cambridge, Mass., 1975.
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THE DYNAMICS OF ECONOMIC FLUCTUATIONS: A FRAMEWORK FOR ANALYSIS AND POLICY DESIGN
Nathaniel J. Mass
4saistant Professor of Management
Alfred P. Sloan School of Management
Massachusetts Institute of Technology, Cambridge, Massachusetts
This paper describes a general framework for
assessing the validity of alternative theories of busi-
ness cycles and longer-term economic cycles.* The eval-
uative framework draws upon a generic model of the pro-
duction sector of the economy As discussed in Section
III of this paper, the production sector model (termed
the "basic production sector") differs intrinsically
from conventional theories of the firm by incorporating
conserved levels of inventories and backlogs which
decouple rates of ordering, shipments, and production;
inclusion of such "buffer stocks" permits treatment of
disequilibrium behavior characteristic of economic
cycles. Evaluation of alternative theories of economic
cycles Is carried out by isolating the central causal
elements of each theory and incorporating those elements
into the basic production sector. Through computer sim-
ulation of the resulting model, the relative importance
of each hypothesized factor can be gauged. The results
of such evaluation should have great value to economic
theorists and policy-makers who are currently confronted
with a morass of partially overlapping and partially
conflicting theories of cyclic economic behavior. Clar-
ification of the underlying causes of economic cycles,
in turn, should contribute to the design of enhanced
policies for economic stabilization.
Section II of this paper expands upon the motiva-
tion for evaluating extant theories of economic cycles.
Section III outlines the principal components of the
production sector model used in the evaluation. Section
IV'applies the evaluative framework to study the role of
labor adjustments and fixed capital investment in gener-
ating economic cycles. As noted in Section IV, the
majority of business-cycle theories, including, for
example, those of John Hicks, Paul Samuelson, and James
Duesenberry, center on the role of fixed capital invest-
ment in the short-term business cycle. However, Section
IV demonstrates that the long delays inherent in plan-
ning, construction, and depreciation of capital equip-
ment render it unlikely that investment in fixed capital
is an intrinsic cause of short-term cycles. Instead,
the analysis suggests that labor-acquisition and short-
term production and inventory-management policies prin-
cipally underlie typical four-year business cycles.
Moreover, capital-investment policies appear to cause
an eighteen- to twenty-year cycle in potential output
resembling the so-called *"Kuznets cycle." Finally, Sec-
tion V summarizes the paper and outlines directions for
future theoretical and policy-oriented research.
'IEee, for example, Garvy (1943).
4Aaberler (1964), p. 361.
THE NEED FOR CRITICAL EVALUATION OF BUSINESS-C,
THEORIES
Empirical studies of the nati 1
identified several cyclical fluctuationsccharecteri^t
of aggregaaterecureconomic behavior. Of these, the
j.
cycler is ring fluctuation of approximately
years ?
duration in output, prices, investment, and u-,,r,
ployment. In the intermediate range of periodicitirs,
the "Kuznets cycle" is an eighteen- to twenty-year f
tuation in'the rate of growth of capital stock and,
therefore, in "potential output."*k Finally, at the
long end of the spectrum, the "Kondratieff cycle" is 4
fifty-year cycle in prices, interest.rates, and capital
investment.***
The volume of empirical research and theoretical
study that has been devoted to each of the three pri-.
cipal economic cycles described above varies widely,
For example, beginning chiefly with the work of Burns
and Mitchell (1946), a wide range of empirical evidence
has been assimilated regarding the timing, periodicity,
and phase relationships characteristic of short-term
business cycles. Numerous theories of the short-tern
cycle have also been advanced. In contrast to the large
number of business-cycle studies, Abramovitz (1961) has
noted that relatively little data or theory describing
the causes and properties of Kuznets cycles is current:-i
available. Furthermore, evidence on the Kondratieff
cycle is-so sparse as to call into question the very
existence of the hypothesized fifty-year cycle.4-
The evaluative framework developed in this paper is
designed to clarify the causes of the business cycle and
the longer-term economic cycles. Clarification of the
causes of business-cycle behavior Is needed precisely
because such a large number of business-cycle theories
have been proposed. As Haberler has observed, "the
analysis-of existing theories of,the cycle has furnished
a number of hypotheses. Few of these seem to be defin-
itely wrong or a priori impossible. What is unsatisfac-
tory, however, is the exclusiveness with which many
writers proclaim one or other of these hypotheses as
the only possible solution."# One objective of the
present work, therefore, is a first effort to integrate
the existing theories of the business cycle in a unified
framework of analysis.
A related objective is the exploration of the
dynamic implications of widely held business-cycle
theories. Are the economic decisions embodied in
*This research is supported under a grant provided by the Rockefeller Brothers Fund. The present paper is a dis-
, "Generic Feedback Structures Underlying Economic Fluctuations,"
tillaAlfredtiP.on Sloan the auSchoolthor's of Ma doctoral nagement, disserMasstaachustionetts Institute of Technology (December 1974). A revised version of
the dissertation is forthcoming under the title, Economic Cycles: An Analysis of Underl... Causes (Cambridge:
Wright-Allen Press, 1975),
**Potential output is defined as the maximum output derivable from the economy's other factors of production. See Okun (1962) for further definition and 1discussion,stocka of labor, capital,
***Fbr detailed discussion of the characteristics of the three cycles, see Gordon (1961), Hansen (1951), and Lee
(1963).
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A
established business-cycle theories actually major
determinants of the four-year cycle? Within"thd basic
production sector, the relative importance of specified
processes or relationships in generating short-term
cycles can be tested. As discussed earlier, evaluation
of alternative business-cycle theories in the proposed
framework proceeds by incorporating the theories under
examination into a common model structure. The relative
validity and importance of each theory can then be
assessed by'analyzing the change in model behavior re-
sulting when the structural elemenas under study are de-
leted or added. 41
To provide a concrete illustration of the theory-
testing process, this paper utilizes the production sec-
tor model to study the role of labor adjustments and
fixed capital investment in generating short-term busi-
ness cycles. As noted by Burns (1969), the predominant
number of. business-cycle theories, including the theo-
ries of Paul Samuelson, John Hicks, Nicholas Kaldor, and
James Duesenberry, emphasize fluctuations in fixed capi-
tal investment as a cause of overall fluctuations in in-
come and output.* Such theories have been widely influ-
ential from a theoretical standpoint, and have stimu-
lated much subsequent business-cycle research. In addi-
tion, widespread acceptance of the theories has led to
formulation of economic stabilization policies designed
to regulate investment opportunities. However, compared
with other 'factors of production such as labor or in-
process koods, fixed capital has a relatively long aver-
age lifetime, and is characterized by long lead times in
planning, financing, and construction of new projects.**
The long time constants associated with fixed capital
investment and depreciation suggest that fixed capital
variations cannot be a basic cause of short-term busi-
ness cycles: Abramovitz has concisely presented a heu-
ristic argument for this position:
For a number of reasons, the simpler capital-
stock adjustment models with their implied re-
quirements for balanced growth rate take on
heightened interest when considered in the
context of long swings rather than in that
of shorter business cycles. First, insofar
as these models treat investment as dependent
in part on current or past changes in the de-
mand for finished goods, there has always
been justifiable skepticism about their ap-
plicability to durable equipment and struc-
tures, so long as the theory was supposed to
illuminate investment movements in short cycles.
Since investment in durables is made for long per-
iods of time it is doubtful whether it would re-
spond readily to income change over short periods.
This difficulty disappears, however, when we con-
sider expansions lasting 8 to 12 years or more.***
According to Abramovitz, then, fixed capital invest-
ment is unlikely to bean essential factor in generating
the short-term cycle, since the delays in capital formu-
lation have about the same magnitude as the four-year
business cycle and the delays in capital depreciation
run much longer. The statement that fixed capital in-
vestment is not essential in generating the business
cycle has two principal dimensions: first, that busi-
ness cycles can occur independently of changes in fixed
capital investment; and second, that fixed capital vari-
ations cannot independently generate four-year cycles.
Section IV of the paper shows, for example, that, if
fixed capital stock does not vary, short-term production
and inventory-management policies governing labor acqui-
sition still generate four-year cycles. Moreover, Sec-
tibnIV indicates that four-year business cycles do not
appear in an economy where fixed capital is the only
variable factor of production. These results demon-.
strate that fixed capital variations cannot be an in-
trinsic cause of four-year business cycles. More broad-
ly, the results illustrate the use of the proposed eval-
uative framework for discriminating among alternatiye
theories of the business cycle.'
With regard to the longer-term economic cycles,
analysis of the basic production sector within the pro-
posed framework reveals that fixed capital investment
may underlie the observed eighteen- to twenty-year
Kuznets cycle.+ Such a conclusion is consistent with
the previous quotation from Abramovitz; moreover, the
results broadly illustrate the potential of the proposed
evaluative framework for generating insights about pre-
viously unstructured systems and unexplained modes of
behavior.
III. OVERVIEW OF THE BASIC PRODUCTION SECTOR
Figure 1 provides a brief overview of the roduction
sectbr model used in the evaluative framework .4 The ba-
sic production sector is a generic model of a producing
unit within a national economy. The sector receives or-
ders which accumulate in an unfilled order backlog.
*See Samuelson (1939), Hicks .(1949), Kaldor (1940), and Duesenberry (1958), for the original statement of these
theories.
**Evans (1969) describes the delays in planning for and obtaining new fixed capital in terms of an "administrative
lag" and an "appropriations lag." The administrative (decision) lag subsumes the time required to formulate ac-
tual investment plans; the appropriations lag intervenes between appropriation and actual investment expenditures.
Evans estimates the sum of the two lags at about two years.
***Abramovitz (1961), p. 537. in R. A. Gordon and L. R. Klein, ed., Readings in Business Cycle Theory (1965).
4Xass (1975), Chapter 4, further suggests that capital-production behavior may underlie long-term cycles. in the
periodicity range of the Kondratieff cycle.
The production sector model is a simplified version of the production sector of the national socio-economic model
.under construction by the System Dynamics Group at MIT. For a description of the overall objectives and focus of
the project, see Jay W. Forrester, "Understanding Social and Economic Change in the United States," Proceedings of
the 1975 Summer Computer Simulation Conference, San Francisco (July 1975).
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Eased upon its production capacity and inventory and or-
der backlog levels, the sector generates a shipment, rate
of output; the shipment rate depletes both inventoty and
order backlog. The production sector also formulates an
output decision based on the adequacy of inventories and
on the magnitude of the sector's order backlog. Desired
production rate, in turn, along with desired factor pro-
portions, governs the sector's desired inventories of
factor inputs such as labor and capital.* The discrep-
ancy between actual and desired factor inventories con-
trols acquisition (ordering) of factor inputs. Finally,
the sector's available factor inventories determine pro-
duction rate.**
Figure 2 provides a more detailed view of the
structure of the production sector. At the left of the
figure, production rate is determined by the available
stocks of labor and capital.+ Production rate adds di-
rectly to inventory and also affects shipment rate, with
shipments rising with increased production capacity.$
? The production rate decision forms the nucleus of
the production sector model. In the sector model.
DPROD - Desired production (output units/year)
APROD - Average production (output units/year)
DINV - Desired inventory (output units)
INV - Inventory (output units)
BL - Backlog (output units)
DBL - Desired backlog (output units)
TCIB - Time to correct inventories and backlogs
(years) .
Equation (1) dictates expansion of output--an increase
in production above the recent average production rate-
whenever the sector's desired inventory exceeds avail-
able inventory or when backlogs are deemed excessively,
PRODUCTION
RATE A INVENTORY
LABOR
. ~ 4
ORDERS FOR
LABOR
BACKLOG
DESIRED FACTOR
PROPORTIONS
.s .
Figure 1. Feedback structure governing levels of labor and fixed capital.
*For sihoplicity, only two factors.of production, labor and fixed capital, are considered in the analysis. Labor
and capital are chosen as contrasting factors because labor is typically acquired readily and has a comparatively
short lifetime within the firm while, as discussed previously, capital is a durable asset characterized by long
planning and construction delays.
**As described in Mass (1975), Chapters 3 and 4, utilization of factor inputs is considered variable, depending on
the balance of production and desired production within the sector.
+The production function actually utilized is a Cobb-Douglas function, modified to account for variations in
capac-ity utilization. See Mass (1975), Chapter 3.
iShipment rate in the model is also affected by inventory and backlog levels. 'Therefore. for example, by inven-
tories tend to curtail shipments (or, equivalently, raise delivery delays) while large order backlogs create pres-
sures to expand shipments.
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r
RATE^v4 ~-~__-- INVENTORY
large. The coefficient TCIB controls the rate at which
the sector attempts to eliminate inventory or backlog
discrepancies.*
+DESIRED C PITAL/
MARGINAL COST
OF CAPITAL
assumed to equal average production rate APR multiplied
by normal inventory coverage NIC. In the economics lit-
erature, desired inventories are typically assumed to
depend on production or sales as a reflection of the
level of activity of the firm. The motives for holding
inventory have been described as follows by Ruth Mack:**
1. Bridging the time rqquired for processes (eco-
nomic transformations) to be performed
Figure 2. Simplified causal loop diagram of two-factor input model.
2. Efficient production or purchasing lots
A
INVENTORY
MARGINAL COST
OF LABOR
3. Insurance against losing sales because of fluc-
tuations in demand or other matters
4. Smoothing operations by provision for more or
less foreseeable fluctuations
5.*Crasping the potential advantage (or avoiding the
disadvantage) of actual or expected changes in
conditions in markets in which purchases or sales
are made
6. Providing elective freedom from the tyranny of
planning for uncertain events
Most of the six motives for holding inventory cited by
Mack do not differentiate clearly the desirability of
The inclusion of inventory and backlog correction terms in the equation for desired production appears consistent
with results of recent econometric research. For example, Mack (1967) and Fromm (1961) conclude that desired in-
ventories and unfilled orders both exert a significant impact on inventory investment. In addition, Darling
(1959) found that inventory investment varies positively with sales and with changes in unfilled orders. Also,
see Stanback (1962), p. 41, and Zarnowitz (1961), pp. 426, 451.
**Mack (1967), p. 27.
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it
basing desired inventory on production rate versus sales
rate. Certain of the motives, however, appear to favor
relating desired inventory to production rate.' For ex-
ample, desired stocks of purchased materials and goods
in process should depend on average production.* In ad-
dition, inventory ordering in most corporations is con-
ducted by those directly involved in production. There-
fore, in the production-sector equations, desired inven-
tory is based on average production rate. This formu-
lation may be regarded as an approximation to a more
complex underlying structure that depends on both aver-
age production and sales. ,.
Desired backlog DBL is assumed to equal average --
production rate APR multiplied by normal backlog cover-
age NBC. DBL therefore represents the order backlog
that would prevail if production and shipment rate were
both equal to average production and delivery delay were
equal to a normal value of NBC years. The correspon-
dence between normal backlog coverage and normal deliv-
ery delay can be seen in the definition of delivery
delay:
Delivery delay - Backlog/Shipment rate.
The backlog correction term in Equation (1) therefore
indicates whether, given the sector's current production
capacity, orders in backlog can be filled in more or
RATE
TO 'Ti
INCOMING
ORDERS
Figure 3. Inventory loss caused by increased sales.
*For example, Lovell (1961) bases desired stocks of purchased materials and goods in process on production rate in
an econometric model of inventory investment.
**For example, see Samuelson (1939) and Arrow and Nerlove (1958). '
4The term "amplification" refers, in the case of production, to the observed tendency for output to fluctuate by
much more than sales or incoming orders over the typical business cycle. See Forrester (1961) for more precise
definition. For empirical evidence on production behavior over the business cycle, see Gordon (1961), Haberler
(1964), and Hanson (1951).
#Note that the analysis in Figure 3 ignores backlog behavior for simplicity and, further, assumes that shipments
(sales) equal incoming orders. Section IV elaborates upon this example.
'less time than the normal delivery delay. The sector at-
tempts to expand capacity when backlogs are excessively
large, and to contract capacity when backlogs are low.
The dynamic and behavioral significance of the in-
ventory and backlog correction terms in Equation (1) for
desired production merit discussion at this point. z
Dynamic models in the economics literature typically
ignore the accumulation of production and orders iq in-
ventories and backlogs, respectively.** For example,
rather than measuring the supply of goods by available
inventory stocks, such models treat supply as a produc-
tion flow rate governed by marginal costs of production.
Analogously, demand is considered as a flow of purchases
(consumption), rather than as a .level of unfilled orders.
Finally, price changes are typically assumed to occur
whenever supply and demand, measured as rates ofproduc-
tion and consumption, are imbalanced. Such a represen-
tation of supply and demand, however, fails to capture
the disequilibrium behavior, and, in particular, the am-
plification, of production activity, characteristic of
business cycles.4-
To understand this deficiency of traditional eco-
nomic models, consider the response of inventories and
production within a firm or industry to a step increase
in incoming orders. As shown in Figure 3, as orders
increase, pressures arise to expand production. The
INVENTORY
I J
1/
S_ I
PRODUCTION I
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increase in production rate is consistent with the clas-
sical economic analysis. However, consider point tl in
Figure 3 where production has risen to equal consumption
(orders). According to the classical model, supply and
demand are equal at this point, and no further pressure
on output or price should be exerted. However, all dur-
ing the period to to tl (in which production remained
below incoming orders), inventories have been depleted.
The total inventory loss over this interval is equal to
the integral
1 (Orders - Production) dt,
which measures the accumulated excess of consumption
over production. In Figure 3, this integral is repre-
sented by the shaded area between the production and
consumption curves. Therefore, at point tl, supply
equals demand in the rate-of-flow sense--production
equals consumption-but inventory is below desired in-
ventory.* Such an inventory imbalance would necessitate
additional expansion of output beyond the incoming or-
der rate, and would probably exert continued upward
pressure on price. Therefore, the classical model of
supply and demand-which ignores inventory and backlog
? behavior fails to represent adequately the determinants
of pricing behavior and, further, fails. to capture the
amplification and necessary overshoot of production en-
gendered by-changes in orders or consumption. These
issues are discussed further in Section IV of the paper.
Referring once again to Figure 2, desired produc-
tion, together with the desired capital/labor ratio, de-
termines the desired stocks of capital and labor. The
formulation'resembles the neoclassical investment func-
tion described by Jorgensen (1967).** Comparison of the
actual and desired stocks of capital and labor yields a
discrepancy which modulates orders for the two factors.
Finally, orders for factor inputs, after a delivery (ac-
quisition) delay, add to the levels of capital and la-
bor, respectively, thereby altering production
capacity.***
IV. EXAMINATION OF THE ROLE OF LABOR ADJUSTMENTS AND
CAPITAL INVESTMENT IN THE BUSINESS CYCLE
Section IV applies the evaluative framework out-
lined in Sections I-III to study the role of fixed capi-
tal investment and labor-hiring policies in generating
short-term business cycles. Such an evaluation appears
necessary because of the dominant emphasis in the liter-
ature and in policy debates on capital-investment theo-
ries of the short-term cycle. Section II developed the
argument, however, that capital investment is unlikely
to be an essential cause of the business cycle due to
the relatively long delays associated with acquisition
and depreciation of capital plant and equipment. As an
alternative to'the capital-investment theory, then, we
might propose that variations in readily-acquired and
relatively short-lived factors such as labor principally
underlie the business cycle. In terms of the argument
of Section II, the relatively short delays involved in
labor recruitment and turnover suggest that labor adjust-
ment could be an intrinsic cause of the cycle.
In order to investigate the above hypotheses, Sec-
tion IV develops a sequence of three computer simula-
tions. For the first simulation, labor is considered as
the only variable factor of production. The resulting
simulation exhibits a four-year cycle in production, em-
ployment (labor), and inventory. The second simulation,
which considers capital as the only variable factor in-
put, exhibits approximately a fifteen-year cycle in pro-
duction rate and in the level of capital equipment. Fi-
nally, a third simulation, including both labor and cap-
ital as variable factors of production, exhibits the
four-year production, employment, and inventory cycle
characteristic of labor adjustments superimposed on a
longer-term cycle in capital and potential output. This
analysis verifies that the periodicities associated with
adjustments in labor and fixed capital are sufficiently
far apart that the individual cycles remain distinct
when labor and capital combine as joint factors of
production.
Figure 4 illustrates the response of the production
sector, with labor as the only variable factor of produc
tion,to a 15% step increase in consumption (orders).
This simulation is intended to isolate the periodicities
associated with labor-hiring and termination policies.
The consumption increase begins after one-half year (at
time - .5).'*? Until time - .5, the system remains in
equilibrium with production equal to the exogenous con-
sumption (incoming order) rate of 3 million units per
year. Also, labor, inventory, and backlog equal their
desired values. Figure 4 exhibits approximately four-
year fluctuations in labor, inventories, and production.
The four-year period corresponds quite closely to the
average 49-month period cited by Arthur Burns as charac-
teristic of American business cycles.*
In Figure 4, as consumption jumps from 3 million to
3.45 million units/year, backlog starts to rise; the
*Desired inventory would probably rise over the interval to to tl, reflecting both increased production and sales.
The increase in desired inventory would tend to accentuate further the inventory discrepancy arising at time cl.
**Also. see Jorgensen, Hunter, and Nadiri (1971) and Bischoff (1971). Mass (1975), Chapters 4 and 5, describes sev-
eral differences between the "ordering function 0 utilized in the basic production sector and the neoclassical
model.
***The delivery delay for factor inputs is not shown explicitly in Figure 2.
+As discussed by Forrester (1961) a simple test input such as a step input or random noise can excite the periodic-
ities inherent in a system. Section 3.7 of Mass (1975) describes a model with endogenous consumption based on
wage incomes. This section illustrates that multiplier-accelerator interactions discussed widely in the litera-
ture appear less fundamental in generating economic cycles than amplification produced by inventory- and backlog-
management policies. See Samuelson (1939) for an overview of the multiplier-accelerator theory of business cycles.
The production sector model with labor as a single variable factor input exhibits a cycle that is consistently in
. the three- to five-year range when model parameters are varied by +100X.
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? ? ? 0+~1 ? ? . ? ? ? ? 1 ? ? ? ? ? ? ? ? ? 1 ? ? ? ? ? ? ? ? . 1
oOGO N in
OOO ? _ ? In
- If N
Figure 4(a)
Figure 4. Step response of basic production sector.
increased backlog raises the shipment rate, thereby de-
pleting inventory. Inventory declines from an initial
value of 1.5 million units to approximately 1.45 million
units at the end of the first year. over the same time,
desired inventory rises to 1.55 million units. Backlog
increases from .6 million units to about .75 million
units at time 1.5, while desired backlog rises over the
same interval from .6 million to .65 million units.
The resulting divergence between actual and desired
inventory and between actual and desired backlog causes
a rapid expansion in desired production. Figure 4(b)
shows desired production rising from 3 million units/
year to a peak value of 3.6 million units/year at
year 2. The rise in desired production causes a cor-
responding rise in desired labor from 1500 men to ap-
proximately 1850 men at year 2.
In Figure 4(a), production rises to a maximum value
of about 3.9 million units/year in response to the in-
crease in desired production. The increase in produc-
tion at this point over the initial value of 3 million
units/year is .9 million units/year, or double the in-
crease in incoming orders. The peak in production
slightly lags desired production due to the delays in
acquiring labor. This lag isrsomewhat mitigated, how-
ever, by the use of overtime, instead of additional
hiring, to expand production. For example, Figure 4(b)
shows that the relative length of work week rises to a
value of'1.07, implying a 7% increase in the average
work week, at the start of the second year. Production
rate exhibits a four-year period between years 2 and 6.
The production cycle is caused by inventory and backlog
policies that induce successive overshoot and under-
shoot of'production relative to consumption.
?
In Figure 4'(a), as long as the rate of production
is below consumption and shipment rate, inventory con-
tinues to decline and backlog continues to accumulate.
Consequently, inventory reaches a minimum value, and
backlog approximately attains a maximum value at the
point where production rises to just equal consump-
tion.* This characteristic behavior ofproduction rate
*In actuality, Figure 4(a) shows that backlog peaks roughly one-half year after production equals consumption. The
slight lag occurs because shipment rate is constrained by low inventory; therefore, the shipment rate only equals
Consumption at time 1.5.
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A
I 0 0! 8
0 0
O N N
W N
fn
and inventory is displayed in Figure 5. Figure 5 shows
an expansion of production resulting from an increase
in incoming orders occurring at time to; production
rises until it equals the incoming order rate at time
t1. However, at time tl, inventory is below, and order
backlog above, their desired values. These discrepan-
cies necessitate a continued expansion of production
above the incoming order rate. In other words, even
when production equals incoming orders, expansion
must continue in order to eliminate the inventory
shortage and large backlog accumulated while produc-
tion was still less than the incoming order rate.
For this reason, the computer output in Figure 4 shows
that desired production rises above consumption at the
start of the second year; desired production continues
to remain above orders until approximately year 3.*
Figure 4(b)
? . In a firm or in an entire economy, if labor and
production continually expand as long as inventories
are short, for example, the pattern illustrated in
RELATIVE LENGTH
OF WORK WEEK
1
1 1
1
/ 1
U1
? O
Figure 6 appears. In Figure 6, production expands in
response to an increase in incoming orders until in-
ventory builds up to equal desired inventory.** How-
ever, at the point where inventory equals desired in-
ventory, production exceeds incoming orders. Inven-
tory therefore continues to rise above desired inven-
tory. The resulting inventory surplus can only be
eliminated if production falls below incoming orders
for some period of time. In this way, inventory adjust-
ments lead to production fluctuations around the incom-
ing order rate. Backlogs similarly exert a destabiliz-
ing effect on production rate, thereby accentuating
the effect of inventories. Output must rise above
incoming orders to eliminate the large backlogs accum-
ulated during the initial upsurge in demand. The re-
sponse of production to backlog behavior could be ana-
lyzed in a manner parallel to the response shown in
Figure 6 for the case of inventories.
*For a detailed verbal and graphical analysis of the causes of inventory fluctuations in a simple second-order
inventory-workforce model, see Mass and Senge (1974).
**Note that the swings in production would be accentuated if desired inventory Is assumed to rise with increasing
production or sales.
r ~ 1
V 1 , '??
DESIRED LABOR
I. 1 DESIRED/ PRODUCTION 1
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DESIRED INVENTORY,
DESIRED BACKLOG
INCOMING ORDERS
PRODUCTION
RATE
Figure 5. Inventory and backlog discrepancies arising from an increase in incoming orders.
The fluctuations in production in Figure 4 are con- after the 15% step increase. The damping ratio charac-
vergent over time. Such convergent behavior is reason- terizing production [defined as (1 - the ratio of suc-
able since the consumption rate is perfectly constant cessive peaks)] is approximately 55%, indicating that
I 'I
t DESIRED / I
INVENTORY I / i I
f/ INCOMING ORDERS
i I
/
?
1 I
1 I
PAOE DUCTION
f
TO
Figure 6. Increase of production above incoming orders.
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? A
ft
55Z of the overshoot of production is eliminated in each
successive cycle.*
The phase relationships seen in Figure 4 appear to
correspond closely with available statistical evidence
on business cycles. For example, in Figure 4(a), back-
log leads production by approximately one-half year.
Backlog peaks before production since backlog begins
to decline once shipment rate exceeds consumption;
in contrast, production continues to expand beyond
consumption, as discussed earlier, in order to build
up inventory and reduce backlog to desired values.
The one-half year lead of backlog with respect to
production conforms closely to evidence presented in
Zarnowitz (1961) and Stanback (1961).
Figure 4 also shows a slight lag--roughly-one-
quarter to one-half year in duration-of labor behind
-production. Production declines even while labor is
increasing because use of overtime declines (seen in
Figure 4(b) as a declining relative length of work
week) as production begins to exceed desired produc-
tion. Therefore, in Figure 4, hiring rate peaks at
year 1.5, but labor continues to expand because the
hiring rate still slightly exceeds the termination
rate (not plotted). The brief lag. of employment be-
hind "reference cycle" peaks is discussed in Gordon
(1961), p. 289.**
B. Economic Cycles Induced by Fixed Capital Investment
Figure 7 exhibits the response of the basic produc-
tion sector including fixed capital as a single variable
factor of production to a 15% step increase in consump-
tion beginning at year 2.**** All system variables
exhibit a cycle of approximately fifteen-year perio-o
dicity.*****? Such a periodicity is well beyond thd,
range of short-term business cycle fluctuations, but
closely resembles the periodicities characteristic of
long-term Kuznets cycles. The Kuznets cycle, according
to Hickman, is a fifteen- to twenty-year fluctuation in
the rate of growth of capital stock, output, productiv-
ity, and other variables.4- The-Kuznets cycle is also
characterized by long swings in growth of labor force
and unemployment rate. Figure 8 illustrates average
annual changes in output for the United States from
1860 to 1960. Figure 8 shows" Kuznets-cycle peaks oc-
curring roughly in 1865, 1885, 1900, 1920, and 1940.$
Detailed analysis of the results in Figure 7 com-
pletely parallels the analysis of Figure 4, except
that the response is drawn out over a much longer
period and the magnitude of lead and lag relationships
consequently differs widely. Nonetheless, a brief
analysis is provided here to emphasize the parallels
between causes of oscillations respectively induced
by labor, and fixed capital.
Finally, Figure 4(a) shows a one-year (quarter-
cycle) lag of inventory behind production. Since ship-
ment rate tends to lag production slightly, inventory
lags shipment rate by about three-quarters of a year--
a period very close to the 7-9 month lag cited by
Abramovitz for manufacturing industries.*** Inventory
tends to lag production because inventory continues
to increase, even.while production declines, as long
as production exceeds shipment rate. Such a time-
pattern of inventory behavior is observable in the
aggregate economy as well as in many individual
industries.
In Figure 7, as incoming orders increase, inventory
begins to decline and order backlog increases. Desired
production [plotted in Figure 7(b)] rises as a result,
thereby leading to increased orders for capital. How-
ever, the lengthy planning and construction delays for
fixed capital delay the increase in actual capacity
acquisition. By around year 5, production has increased
sufficiently to equal consumption, thereby terminating
the drop-off in inventory. But inventory has been
steadily depleted between years 1 and 5, while desired
inventory has risen in response to increased production.
At year 5, for example, inventory equals 1.25 million
*Production peaks at a value of 3.9 million units/year at time 2 and 3.65 million units/year at time 6. The
damping ratio, defined relative. to the mean point of the oscillation, is therefore:
_ (3.65 - 3.45)
(3.9 - 3.45) .
**Reference **Reference cycles have been analyzed by the National Bureau of Economic Research to identify turning points
in general business activity. For a brief description of the approach, see Gordon, pp. 265-270.
*****The basic production sector including fixed capital also responds with a fifteen-year cycle to random noise
in consumption. The result probably has greater practical significance than the step or ramp responses il-
lustrated above, because random variation is necessarily superimposed on all consumption streams.
4-Hickman (1963), pp. 490-492. The original empirical work supporting the existence of 18-20 year swings in
capital growth appears in Wardwell (1927) and Kuznets (1930). Lewis and O'Leary (1955) have conducted a
more recent study indicating the existence of Kuznets-type cycles in a variety of countries.
4As mentioned above, Kuznets-cycle fluctuations appear in the rate of growth of output and capital stock.
Such fluctuations superficially differ from the capital-production cycle illustrated in Figure 7 which
exhibits a cycle in absolute levels of output and fixed capital. However, available data on the Kuznets
cycle are-drawn from a growing economy and therefore measure fluctuations in output and capital around a
long-term growth trend. To produce comparable data, the basic production sector can be subjected to a
steady ramp increase in incoming orders. Resulting simulations exhibit a fifteen-year cycle in capital
growth rate, identical to the periodicity of capital in Figure 7. } K `
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INVENTORY 1 PRODUCTION
DESIRED 1
,INVENTORY 1
M bbOc'
1? a ? e
r- Ln
f r N
Figure 7(a)
Figure 7. Step response of basic production sector including fixed capital.
units while desired inventory equals nearly 1.7 million
units ["see Figure 7(a)]. Analogously, Figure 7(a) ex-
hibits a large backlog discrepancy at year 5 with back-
.log equal to .9 million units and desired backlog equal
to .66 million.
To eliminate the inventory and backlog discrepan-
cies caused by increased consumption, production must
rise above consumption. This, in Figure 7(b), capital
rises from an initial value of 7.5 million units to
about 10 million units at year 10. Capital continues
`to expand as long as desired production exceeds aver-
age production. However, as inventory builds up once
more and backlog declines, desired production rate
drops off, thereby gradually leading to excess capacity.
Capacity remains in excess over several years as a con-
sequence of the long delay in capital depreciation.
Consequently, Figure 7 displays a cyclical adjustment
similar to the behavior in Figure 4 where labor was
considered the only variable factor of production.
However, the response is protracted compared with the
four-year cycles induced by labor adjustments.* Com-
pared with Figure 4, addition of capacity is delayed
on the production upturn due to increased acquisition
delays; moreover, capacity is slowly reduced on the
downturn as a result of gradual "runoff" of capital
through depreciation.
The capital and production cycle in Figure 7,
although considerably longer than the four-year business
cycle, probably still lies on the short range of cycles
induces by fixed capital investment. For example, the
production sector underlying Figure 7 resembles an in-
dustrial sector producing consumer goods. A consumer-
goods sector is characterized by a relatively short
delivery delay for its output'and, also, by a relatively
short delay for in-process inventory between initiation
and completion of production. Consequently, a consumer-
goods sector normally experiences short delays in ad-
justing production to consumption. In order to study
the behavior modes characteristic of a capital-producing
sector, rather than a goods sector, the parameter values
of the sector model can be adapted to describe a capital
sector. Compared with the goods-producing sector, the .
capital sector is assumed to have a longer manufacturing
and delivery delay for its output. Due to the increased
*Pigou and D. H. Robertson both attributed the period of business cycles to the "gestation delay" or construction
period of capital equipment. The results in Figure 7 indicate the role of such construction delays, in addition
to planning and depreciation delays, in generating capital cycles. However, contrary to Pigou and Robertson, cy-
cles induced by fixed capital investment appear to have a much longer period than the four-year trade cycle.
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A
? V11
is N n
o?-0 1 I ? , I
in N ; , L. _ DESIRED CAPITAL
1 1 1
F N
O At O
O?
O ?
ORDERS FOR
CAPITAL 1 1
1 1 1
C G O
N O
Figure 7(b)
delivery delay, the capital sector also takes longer to
correct inventory and backlog discrepancies. Moreover,
the capital sector is assumed, to take longer to adjust
production due to fears of overbuilding capacity if ad-
justment proceeds too rapidly; such risks of overexpan-
sion tend to increase rapidly as the delivery delay of
the sector increases. When the appropriate parameter
changes are incorporated, the production sector exhib-
its roughly a twenty-year capital cycle.* In a model
of the economy containing both goods-producing sectors
and capital-producing sectors, the long-term capital
cycles characteristic of the individual sectors would
probably be mutually entrained to form a single capital
cycle of around eighteen-year periodicity.**
In terms of the discussion of Section II, the re-
sults described here cast doubt upon the validity of
any theory centered around fixed capital investment
as an essential cause of the short-term businesss cycle.
Instead, the results suggest that labor adjustments
chiefly underlie short-term cycles in output and employ-
ment, while fixed capital investment generates longer-
term cycles in growth of capital stock.
The practical and theoretical significance of these
issues is well described by Gordon:
Economists have not yet developed a gener-
ally. accepted explanation of these intermedi-
ate swings, nor is there full agreement that
these swings constitute a separate order of
? cycles distinct from business cycles. One un-
certainty arises from the fact that these "cy-
cles" are obviously related to the severe de-
pressions of the past century. It is not sur-
prising that expansion should be particularly
**The capital cycle exhibited by the aggregate economy might even be much longer than eighteen to twenty years in
a model which contained structural elements missing from the basic production sector analyzed in Figures 4 and 7.
For example, a model containing a limited supply of labor should tend to exhibit a longer-term capital cycle.
since more of the burden of adjusting production to desired production would be accomplished through capital
ordering rather than through short-term changes in employment. Incorporation of a limited labor supply in the
sector model could well extend the period of the long-term capital cycle close to the fifty-year span of the
Kondratieff cycle. Examination along these lines is currently being conducted within the framework of the
basic production sector.
DESIRED PRODUCTION
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300
200
100
80
60
40
8
4
0
-4
300
200
100
80
60
40
Figure 8. Long swings in aggregate production in the United States.
? (Source: Hickman (1963),?p. 49],)
rapid as the economy comes out of a deep depres-
sion, and the "downswings" of these long cycles
may reflect in part the fact that we have exper-
ienced severe depressions. It is significant,
however, that in the past, deep depressions have
been associated with substantial retardation in
the rate of growth of output.*
From a theoretical standpoint, the results presented
above suggest a common structure underlying both busi-
ness cycles and longer-term capital cycles. Moreover,
according to this analysis, differences in character-
istics of factors of production--differences such as
average factor lifetimes and delivery delays which can
be represented simply in terms of changed parameter
values--suffice to explain the different periodicities
of fluctuation.
C. Economic Cycles Induced Jointly hX Labor and
Fixed Capital
A final computer simulation, shown in Figure 9,
integrates the preceding analysis. Previous simulations
(Figures 4 and 7) dealt with capital and labor individu-
ally in order to study the cyclical modes arising from
each factor input. The simulation in Figure 9 combines
labor and capital in a joint production process.
Figure 9 primarily investigates the question: "When
capital and labor are combined, do the periodicities
associated with each input factor remain distinct or
are they mutually entrained to yield a single cycle of
intermediate length?"
Figure 9, which plots fixed capital stock, labor,
and production rate over a one-hundred-year period,
clearly illustrates the different periodicities asso-
ciated with labor and fixed capital; these results
are in accordance with the analyses conducted pre-
viously on models containing single factors of pro-
duction. The results lend further support to the
hypothesis that labor adjustments principally under-
lie short-term business cycles and that fixed capital
investment is not an intrinsic factor in generating
business cycles.**
*Gordon (1961), p. 243.
**The business cycle is in fact characterized by short-term fluctuations in capital spending,. Such observed fluc-
tuations are consistent with the behavior of the revised production sector model (orders for capital were nqi
plotted in Figure 9). According to the model, short-term investment cycles are the result of fluctuations in the
relative balance of capital and desired capital within the economy. Fluctuations in capital relative to desired
capital stock in turn reflect short-term changes in the balance of production and desired production caused by
corporate policies governing overtime and labor adjustment. In other words, short-term employment and overtime
policies adjust production rate towards desired production over the business cycle, thereby creating varying in-
centives for capital investment. However, the resulting short-term fluctuations in capital investment are direct-
ly caused by the labor policies; capital investment policies still cannot independently generate short-term busi-
ness cycles. Future examination should aim at clarifying further the interactions of production, employment, and
investment
oli
i
h
p
c
es over t
e business cycle.
1486
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Figure 9. Response of two-factor model to noise in production rate--100 years.
D. Implications for Business-Cycle Theory and
Stabilization Policy
The analysis conducted here generally indicates
the importance of reassessing the fundamental assump-
tions underlying business-cycle theory and stabiliza-
tion policy. Many prevalant economic stabilization
policies, particularly monetary policies, are largely
predicated on a capital-investment theory of business-
cycle behavior. However, if business cycles are at-
tributable for the most part to short-term employment
and inventory decisions, policies that attempt to con-
trol fixed capital investment may have relatively little
leverage or at least may be less effective than policies
directly aimed at employment and inventories. Moreover,
if fixed capital investment generates fifteen- to
twenty-year or longer cycles in capital plant, policies
designed to regulate capital investment can have sig-
nificant long-term impacts on output, employment, and
productivity.
The results presented here, although speculative,
suggest the need for critical assessment of proposed
economic stabilization policies according to (1) their
short-term impacts on labor and inventory adjustments;
and (2) their longer-term effects on capital investment
and potential output. Such an evaluation may contribute
to greater understanding of the impacts and probable ef-
fectiveness of discretionary monetary and fiscal poli-
cies and the various "automatic stabilizers."
*For a statement of the monetary theory of business cycles, see Nicksell (1907, 1935), Hayek (1935), and Friedman
V. CONCLUSIONS
This paper has developed a general framework for
analyzing the validity of alternative theories of busi-
ness cycles and longer-term economic cycles. The frame-
work draws upon a general model of production activity
interrelating inventories, backlogs, acquisition of fac-
tor inputs, and output. The production sector model has
been used here to analyze the periodicities associated
different economic factors of production. The results
indicate, contrary to the prevalent capital-investment
theories of *the business cycle, that labor-adjustment
policies, in conjunction with short-term production and
inventory-management policies, appear to underlie the
four-year business cycle; moreover, capital investment
policies appear to be principally involved in economic
cycles of much longer duration. These results motivate
analysis of current and proposed economic stabilization
policies in terms of their short-term effects on employ-
ment as well as their longer-term impacts on capital in-
vestment and potential output.
A wide range of economic processes can potentially
be analyzed within the framework of the basic production
sector. For example, extending the sector to include a
simple monetary sector may help to clarify current de-
bates over the role of money and interest rates in busi-
ness cycles.* Detailed analysis along these lines should
strengthen the foundations of business-cycle theory and,
as a byproduct, enhance the exercise of stabilization
policy.
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VI.
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1489
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WORKFORCE SKILL-COMPOSITION AND. HIGHER EDUCATION IN THE NATIONAL SOCIO-ECONOMIC MODEL
Peter M. Senge
System Dynamics Group
Alfred P. Sloan School of Management
Massachusetts Institute of Technology, Cambridge, Massachusetts
1. BACKGROUND
This paper presents a simple,dynamic model to inves-
tigate basic forces which alter the skill-composition of
the national workforce. The model attempts to identify.
long-term causes for shifts out of "labor" skill-level
jobs and into "professional" skill-level employment in
an industrial country such as the United States. As the
term is used here, a laborer is a worker who engages di-
rectly in the production of some good or in the provision
of a service which does not require highly specialized
training. Laborers therefore include skilled and un-
skilled craftsmen, operatives in manufacturing and ser-
vices, and manual laborers in manufacturing and agricul-
ture. Conversely, professionals include managers; sales-
men; and proprietors; as well as doctors, lawyers, engi-
neers, teachers, and persons in other types of employ-
ment who are commonly referred to as professionals.
The present model focuses on interactions between
workforce composition and higher education. All persons
who receive higher education (schooling beyond that re-
garded as normal during a particular time period) are
regarded as professionals. In the United States, growth
In the professional workforce has been accompanied by
expansion of institutions of higher learning and increas-
ing enrollments of young adults in such institutions.
The workforce-composition model attempts to investigate
feedback interactions between workforce composition and
higher education. The model investigates the impacts of
expansion in opportunities for higher education on the
mix of laborers and professionals in the nation. The
model also attempts to explain how, in turn, changing
-workforce composition generates increased or decreased
demand for higher education.
The model focuses on long-term changes in two var-
iables in particular. The "fraction of the workforce in
professional" provides a measure of workforce composi-
tion. According to data presented by P. M. Blau and
0. D. Duncan, the fraction of the workforce with pro-
fessional skills in the United States rose from about
.18 in 1900 to approximately .35 in 1960.* The model
also attempts to generate plausible behavior for the
fraction of the student-age workforce in higher educa-
tion, called the "fraction in higher education." The
US Office of Management and Budget estimates that the
fraction of adults 18 to 24 years old enrolled in under-
graduate education equaled .24 in 1970.** Although no
historical data series on enrollments in higher educa-
tion seems to exist, the fraction in higher education
appears to have risen continuously over the past thirty
-years or more.
The model of workforce skill-composition summarizes
certain issues being investigated in the current national
modeling project being conducted in the System Dynamics
Group at MIT. The national model attempts to explain
short-, intermediate-, and long-term patterns of economic
and social change in the United States over the period
1850 to 2100.4- The model presented in this paper iso-
lates a small number of the long-term issues which are
important within the scope of the-national model.
The relative availability of labor and profession-
al workers to producing sectors in the national model
will affect the rate at which many model sectors can
grow. Relative shortages of professionals may constrain
growth in certain sectors during early stages of national
growth, and shortages of laborers may be important during
later stages of growth. Therefore, the long-term shift
out of labor into professional may be a significant as-
pect in understanding growth of the national. system.
The growth of the knowledge sector (representing col-
leges and universities, research institutes, and research
and development divisions of firms) is also an important
long-term dynamic in the national model. A major factor
driving growth of the knowledge sector is demand for higher
education. Therefore, the model presented below represents
an initial attempt to understand interactions between de-
mand for higher education and changing workforce composi-
tion, which must be treated in the national model. Under-
standing generated in the present model will contribute to
how these interactions are represented in the national model.
The model presented below simplifies many complex
interactions in the full national model. The model in-
corporates numerous exogenous variables, such as popu-
lation, technological complexity, and relative demand
for laborers and professionals in the nation, which are
part of the feedback structure of the full national mod-
el. The model also assumes certain variables to be con-
stant which in fact vary in the full national model.
Such simplifying assumptions are made in order to permit
the present model to focus on a small set of feedback
interactions which appear to be important in altering
workforce composition over the course of national
development.
II. MODEL STRUCTURE
Section II presents a broad.overview of. the struc-
ture of the workforce composition model. The factors
assumed to alter the mix of laborers and professionals
in the workforce are described in Section II.A. Section
iI.A describes each factor altering workforce composition
in the context ofactual movements of workers in the
Although all factors affecting workforce
described in Section II.A will ultimately be part
of the feedback structure of the full national model,
the present model focuses on feedback interactions be-
tween demand for higher education and workforce skill-
composition. Section II.A also identifies factors alter-
ing the laborer-professional mix, such as promotions and
immigrations, which are assumed to be exogenously
*Data estimated from P. M. Blau and 0. D. Duncan, The American Occupational Structure. Wiley and Sons, 1967 (Figure
1.1. pp. 86-88).
**US Office of Management and Budget, Social Indicators, US Department of Commerce, 1973 (Figure 3/13, p. 87).
4-See J. W. Forrester, "Understanding Social and'Economia Change in the United States," Proceedings of the Summer
Computer Simulation Conference, San Francisco, 1975.
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determined in the present model. Section II.B presents
the feedback structure which describes how thb,demand
for higher education responds to changes in workforce
skill-composition and how the fraction in higher educa-
tion subsequently alters workforce composition.
II.A. Factors Altering Workforce Skill-Composition
The workforce composition model incorporates five dis-
tinct factors which cause changes in the mix of laborers
and professionals in the nation. Pys shown in Figure 1,
workforce composition changes in response to promotions
of laborers to professional, movements of unemployed pro-
fessionals back to labor jobs, immigrations, movements of
(previously unpaid) farm workers to labor, and the ini-
tial entry of young adults into the workforce. Each
source of change in workforce skill-composition corre-
sponds to an actual flow of workers in the economy.
Some of these flows are intra-workforce in character-
that is, the workforce composition changes in response
to movements of labor workers to professional and pro-
CHANGE IN PROFES-
SIONAL FRACTION DUE
TO PROMOTIONS
CHANGE IN
PROFESSION-
AL FRACTION
DUE TO
YOUNG ADULTS
workers experience increasing difficulty, in finding em-
ployment, more are willing to forego professional status
and enter the labor job market. On the other hand,
countervailing pressures (such as the availability of
transfer payments) may keep the unemployed professional
from entering the labor job market as rapidly as supply
and demand conditions would alone dictate.
The entry of new workers into the workforce also
impacts the mix of laborers and professionals. Figure 1
identifies three distinct flows which alter workforce
composition in response to new workers entering the
workforce: immigrations, movements of farm workers to
labor, and young adults joining the paid workforce for
the first time. New immigrants almost always enter the
labor category. Even when immigrants possess profes-
sional-level skills, they are often prohibited from
applying these skills due to language or ethnic barriers.
To grasp the impact of immigration on workforce
composition, consider the following simple example.
CHANGE W PROFES-
SIONAL FRACTION DUE
TO UNEMPLOYED PRO-
FESSIONALS TO LABOR
FRACTION OF WORK-
FORCE IN PROFESSIONAL
CHANGE IN PROFES-
SIONAL FRACTION DUE
TO FARM WORKERS TO
LABOR
CHANGE IN
PROFESSION-
AL FRACTION
DUE TO
IMMIGRATIONS
fessional workers to labor. Intra-workforce shifts in
workforce composition do not alter the overall size of
the workforce. A second subset of worker flows shifts
the laborer-professional-mix as a consequence of new
workers entering the workforce. For example, the ar-
rival of immigrants with labor skills both increases
the overall size of the workforce and decreases the
fraction of the workforce with professional skills.
The two antra-workforce changes in workforce compo-
sition--promotions and movements of unemployed profes-
sionals to labor-represent internal shifts in workforce
composition in response to relative demand for and supply
of laborers and professionals. Experienced laborers move
up to fill managerial positions* more rapidly when em-
ployers have difficulty filling those positions from the
available pool of professionals. Conversely, when an
alundance of professionals are available to fill exist-
ing professional vacancies, relatively fewer laborers
are promoted. The reverse flow of unemployed profession-
als to seek labor jobs likewise responds primarily to de-
mand-and supply conditions. As unemployed professional
If 10,000 new laborers are added to a workforce of
100,000, including 30,000 professionals, the new input
of laborers will alter workforce size and composition.
Workforce size will obviously increase to 110,000. More-
over, the fraction of the workforce with professional
skills will fall to 30,000/110,000, or 27%, as a conse-
quence of adding new laborers but no new professionals
eo the workforce.
The flow of unpaid farm workers to labor also in-
creases the workforce size and alters the professional-
labor mix in the direction of relatively more laborers.
Unpaid farm workers include farmers who were previously
self-employed or in some other way received goods rather
than a wage in payment for their services. The flow of
previously unpaid farm workers to labor includes both
the physical migration of farm workers to urban areas
and the shift of farm workers from unpaid to paid employ-
ment. All farm workers-are assumed to possess labor-
level skills and therefore enter the labor workforce.
As farm workers enter the labor workforce, they alter
workforce size and composition in a fashion analogous
*Note that the term "professional" subsumes managers as well as specially trained professionals in the present model.
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I
to the impact of immigrants on workforce size and
composition.
The impact of young adults on the labor=professional
nix is slightly more complicated than the impacts of
immigrants and previously unpaid farm workers. Com-
pared to immigrants and farm workers, a relatively large
fraction of adults enter the workforce with professional
skills acquired through higher education. Moreover,
the impact of young adults entering the workforce on
workforce skill-composition varies as the fraction of
young adults receiving higher education varies..
A simplified example illustrates the impact of a??
varying student fraction'on the professional fraction.
For convenience, let us call the fraction of young
adults in'higher education the "student fraction" and
the fraction of the current workforce with professional
skills the "professional fraction." Assume that the
fraction.of young adults with professional skills (that
is,:the.student fraction) is less than the current frac-
tion of the workforce with professional skills (the pro-
fessional fraction).* In such a case, the impact of the
flow of young adults entering the workforce on workforce
composition is to reduce the professional fraction in a
manner analogous to the impact of immigrations and the
Demand for higher education is part of a positive
feedback loop affecting workforce composition. As is
indicated in Figure 2, an increase in the fraction of
the workforce In professional leads to an increase in
the demand for higher education, which tends to increase
the fraction in higher education and, in turn, leads to
further increases in the fraction of the workforce in
professional.
s
Young adults demand higher education on the basis
of a variety of factors which reflect their career ambi-
tions and their educational plans. The dependency of
demand for higher education on the traditional fraction
of the workforce in professional represents the role of
family background in determining career ambitions. As
it is used in determining demand for higher education,
the traditional fraction of the workforce in professional
approximates the fraction of professional families in the
nation. For example, if the traditional professional
fraction equals .20, approximately .20 of all young
adults are the children of professionals. Therefore,
inclusion of the traditional professional fraction as a
determinant of demand for higher education represents
the number of young adults drawn to professional employ-
ment by virtue of family background.
farm-worker flow. However, the impact of the student frac- The fraction of young adults aspiring to profes-
tion changes as the student fraction changes. Consider the sional employment also responds to perceived opportuni-
case of 10,000 young adults entering a workforce of 100,000 ties for professional employment. The present model
workers. If there are initially 30,000 professionals assumes that young adults perceive the relative avail-
(that is, a professional fraction of .30) and 1,000 of
the young adults come from higher education (a student
fraction of .10), the professional fraction falls from
.30 to .282 (that is, 31,000/110,000). However, if the
student fraction rises to .20, the flow of 10,000 young
adults into the workforce results in a smaller reduction
of the professional fraction:. from .30 to .291 (that is,
32,000/110,000). If the student fraction continues to
rise until the student and professional fractions are
equal, the entering flow of young adults does not alter
workforce composition. If the student fraction exceeds
the professional fraction, the influx of young adults
increases the professional fraction.
The student fraction varies substantially over the
national life cycle. Section II.B focuses on the factors
assumed to alter the student fraction in the present
model.
Figure 2 presents a causal diagram for the workforce
composition model. As shown in Figure 2, three principal
feedback loops control the mix of laborers and profes-
sionals in the national system. The first feedback loop
represents the decisions of young adults to seek higher
education and the resulting impact of higher education
.on workforce composition. The second feedback loop
shown in Figure 2. describes the impact of promotions on
workforce composition and the reverse impact.of work-
force composition on promotions. The third feedback
loop incorporates the impact of movements of unemployed
professionals to labor on workforce composition.
ability of professional openings by observing the ratio
of orders outstanding for professionals to total orders
outstanding for all workers. The so-called "backlog
ratio" can be thought of as the fraction of all job va-
cancies which are for professional openings. If'the va-
cancies for professional jobs comprise a larger share of
all vacancies than professionals comprise of the total
workforce, the number of young adults who aspire to pro-
fessional employment will increase.
Demand for higher education also depends upon the
perceived appropriateness of higher education as a means
to attain professional employment. One factor which in-
creases the perceived appropriateness of higher education
is technological complexity. As technological complexity
increases, a larger portion of those apiring to profes-,
sional employment see higher education as a desirable or
necessary path to achieve professional employment.
Lastly, Figure 2 shows that the fraction of young
adults who receive higher education depends both on the
demand for higher education and on the capacity of the
knowledge sector to provide higher education. Underca-
pacity in the knowledge sector (too few classrooms, too
few teachers, excessively high tuition fees) restricts
enrollments. ? Excess capacity can expand enrollments to
a certain extent. The relative capacity of higher edu-
cation, shown in Figure 2, measures under- or overcapacity
as a ratio of. capacity in the knowledge sector to demand
for higher education. When relative capacity is less
than unity, the demand for higher education exceeds the
capacity of the knowledge sector. When relative capacity
exceeds unity, capacity of the knowledge sector exceeds
the demand for higher education.**
*A fraction in higher education which is less than the prevailing fraction of the workforce with professional skills
has characterized US history. In 1970, for example, approximately 38% of the paid workforce were professionals
(see'O. D. Blau and P. M. Duncan, op. Sit.) and approximately 30% of young adults were enrolled in institutions
of higher education--four-year colleges and universities, community colleges, and trade colleges. (Source:
(1S'Department of Health, Education, and Welfare, Social Indicators, 1973 ed.)
**In the workforce composition model, relative capacity of the knowledge sector impacts the fraction in higher educa-
tion through the multiplier from capacity of knowledge sector for higher education. The multiplier depends only on
relative capacity of the knowledge sector. The figures showing model behavior in Section III below plot the multi-
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CAPACITY OF KNOWLEDGE SECTOR
RELATIVE CAPACITY OF
KNOWLEDGE SECTOR
/- 1. I-
PROFESSIONALS
TO LABOR
MOVEMENTS OF
FARM WORKERS TO
PAID LABOR
TQCHOLOGICAL
COMPLEXITY
In the present model, capacity of the knowledge sec-
tor is determined as a twenty-year delay of demand for
higher education. The twenty-year delay time in adjust-
ing capacity to demand for higher education represents
the lead time necessary to plan for, finance, and achieve
additional capacity in the knowledge sector. Represen-
tation of capacity as a simple passive adjustment to de-
mand for higher education should be adequate to study in-
teractions of demand and capacity during the period of
growth in demand for higher education.*
The higher education loop incorporates three exogen-
ous variables: backlog ratio, technological complexity,
and student-age young adults in the nation. The backlog
ratio, which measures the relative job vacancies for pro-
fessionals as a fraction of all vacancies, will be used
as a test input in Section III. Technological complexity
is input in the present model as an exponentially in-
creasing function of time. The level of technological
complexity doubles every 30 years. However, the impact
of technological complexity on demand for higher educa-
tion eventually saturates. As a consequence of techno-
logical complexity, the percentage of those aspiring
to be professionals who seek higher education as the
means to professional employment rises from 58% in 1850
to 98% in 1970. After 1970, further increases in tech-
nological complexity only cause the fraction of. young
adults demanding higher education to asymptotically
approach the fraction of young adults aspiring to pro-
sfessional employment..
.The last exogenous variable, the student-age young
adults in the nation, is generated by an aging chain in
the workforce composition model. The aging chain con-
tains five age categories: children (ages-0-14). young
adults (ages 15-24), mature adults (ages 25-44), adults
beyond childbearing (ages 45-64), and senior adults (age
65 and above). The aging chain can be used to generate
a
*In the complete national model. capacity of the knowledge sector will be determined in a separate production sector
of the model: the knowledge sector will expand in response to orders for higher education as well as to orders for
knowledge (technology) from other production sectors in the model. (For an overview of the structure of the generic
production sector, see N. J. Mass, "The Production Sector of the National Socio-Economic Model-?-An Overview." System
Dynamics Group memorandum D-2143, MIT) Representation of capacity by an explicit production sector will permit a
much broader range of responses in capacity of higher education to changing demands for higher education. Although
the present representation of capacity should be adequate for the period of growing demand, representation of capac-
ity as a simple delayed adjustment to demand offers an extremely limited range of dynamic responses when demand
levels off.
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exponentially increasing population which matches US '
population from 1850 to approximately 1915,-of an S-shaped
population pattern which rises to 2.06 million by 1970
and equilibrates at 2.60 million in 2080. The number of
student-age young adults is determined as a constant
fraction of the young adult population.
The feedback loops involving promotions and move-
ments of unemployed professionals to labor in Figure 2
are both negative loops. Each loop incorporates pres-
sures from the overall economy.-to adjust workforce com-
position. These pressures are input through the backlog
ratio in the present model. For example, an increase in
the promotion rate leads to increases in the professional
fraction of the workforce. The increase in the profes-
sional fraction alters the relative availability of labor-
ers and professionals and, unless a further increase in
the backlog ratio occurs, leads to a future reduction in
the promotion rate. The feedback loop controlling the
flow of unemployed professionals back to labor responds
in an analogous fashion to changing availability of labor-
ers and professionals in the nation.
Finally, Figure 2 shows immigrations and movements
of farm workers to labor as exogenous inputs to work-
force composition. Immigrations in the US rose steadily
from 1850 to 1900 and achieved particularly large values
(approximately one million per year) in the years 1900
to 1914.* From that time, immigrations in the US have
fallen'to a present value of approximately 200,000 per
year. The exogenous immigration input in the present
model approximates the historical US data from 1850 to
1970. (Source: US Bureau of the Census, Historical
Statistics for the US, 1960 ed.). Immigrations are as-
sumed to remain constant at 200,000 from 1970 to 2100.
Movements of previously unpaid (that is, self-
supporting) farm workers to labor are likewise input on
the basis of historical data. In the case of movements
of previously unpaid farm workers, the available data
are more imprecise than the immigration data. Data for
rural-to-urban migrations from 1850 to the present is
used as a surrogate for the movements of farm workers
from unpaid to paid labor. Use of such data is inac-
curate because some of those who move from farmstto the
cities are already in the paid workforce and because
persons who shift from unpaid to paid agricultural labor
are excluded from the rural-to-urban statistic. Data
for rural-to-urban migration show a steady increase
from 33,000 migrations in 1850 to 270,000 migrations in
1940; since 1940 rural-to-urban migrations fell to a
value of 200,000 by 1970. (Source: US Bureau of the
Census, Historical Statistics for the US, 1960 ed.)
Movements of farm workers to labor is assumed to contin-
ue falling to a value of 140,000 in 1990 and remain con-
stant from 1990 to 2100.
III. MODEL BEHAVIOR
Simulation of the workforce composition model pre-
sented in Section II shows that the model generates a
pattern of growth in the professional fraction of the
workforce and the fraction of young adults in higher
education similar to that observed historically in the
United States. Section III.A discusses behavior of
workforce composition in the presence of unlimited
exponential population growth. Section III.B investi-
gates the ramifications of equilibration of population
for workforce composition and the fraction of young
adults in higher education. Section III.C shows how,
if given a plausible pattern of behavior, an exogenously
determined relative demand for professional and laborers
(backlog ratio) can accentuate the basic character of
model behavior and bring out an important tradeoff be-
tween maintaining a high internal promotion rate and
providing higher education opportunities for those who
demand them.
=Immigrations to the US fell precipitously during the years of World War I. After the war, immigrations began to
rise toward their prewar level until the Immigration Act of 1921 established quotas on immigrations.
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a,
U.
?
KIIP.r? in u1 WI- r
M M M M I. U. Z U.
U1N in In In 'A 0 U1 U\0r U1 U1 U1 N U1 U1 U1 LA S.r 11
oas, a.tsaa~.rx=.raa.ro,ra.rxxxx
1 CHANGE IN PROFESSIONAL
1 FRACTION DUE TO PROMOTIONS
ri
PROFESSIONALS TO LABOR
CHANGE IN PROFESSIONAL
FRACTION DUE TO UNEMPLOYED.
In a In 1 I
- u 1
. I 'A'pr-
M a. = ~ FRACTION IN
u.
?
FRACTION DUE TO_
IMMIGRATIONS
1 HIGHER EDUCATION
W - O Q
Y. O
U kn
M co
w a. ? ..
I. U.
Q Z
CHANGE IN PROFESSIONAL,
FRACTION DUE ,TO MOVEMENTS ,
OF FARM. WORKERS, TO LABOR ,
CHANGE IN PROFESSIONAL
FRACTION DUE, TO
YOUNG ADULTS,
1 1
i I
O N
O O
N N
LL .
Figure 3(a)
Figure 3. Behavior of Workforce Composition Model Given Unrestricted. Population Growth.
III.A. Unrestricted Population Growth
Figure 3 shows the behavior of the workforce compo-
sition model when driven by an exponentially increasing
population. Figure 3(a) shows the fraction of workforce
in professional, the fraction '(of student-age young
adults) in higher education, and the five rates which
alter the professional fraction. Figure 3(b) shows the
behavior of the exogenously-determined population (the
sum of the five population age categories) and backlog
ratio which drive the workforce model. Figure 3(b) also
presents a variety of variables involved in the feedback
structure which determines the fraction in higher
education.
The simulation in Figure 3 shows two major
checks on growth in the professional fraction--a large
inflgw of immigrants with labor skills and a low fraction
in higher education. Little growth occurs in the simu-
lated professional fraction between 1850 and 1900 as
both these checks combine to offset a large promotion
rate. Promotions contribute the only positive rate im-
pacting the professional fraction. In addition to the
large negative rates influencing the professional frac-
tion due to the influx of young adults and immigrations,
smaller negative rates due tothe flow of unemployed
professionals back to labor and the movements of farm
workers to labor offset promotions.
The balance between promotions, on the one hand,
and immigrations and entering young adults, on the other
hand, lasts until about 1910. The rapid reduction in
the-change in professional fraction due to immigrations
which begins in 1915 removes a major check on growth in
the professional fraction and initiates a prolonged per-
iod of changing workforce composition. As immigrations
na , r,r ~, a a:,::~ ,..rl1 0] 5a1i.e1^. i-. a
~~:;:.,~ ?n.1 of r:n:,
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U ?
dU NN
P1
N m
? ? M H
U UCO-. ~o"
U u U U N"
i
DEMAND FOR HIGHER
EDUCATION
? 1
?
a 1
;rt 1
1~ ?
i POPULATION--4,
? ? . ? ' ? . ? ? ? ? ? ? ? 1
i I
Figure 3(b)
fall, the internal promotion rate pushes the profession-
al fraction upward. Prior to 1910, the large influx of
immigrant laborers offsets a high promotion rate; after
1910 the reduced flow of immigrants permits the profes-
sional fraction to rise steadily.
The elimination of immigrations as an effective
check on growth in the simulated professional fraction
occurs as a result of a reduction in the immigration
rate which drives the present model. As was noted in
Section II.B, an historical reduction in the flow of
immigrants into the US occurred in 1915 (see preceding
footnote).*
Although immigrating laborers cease to be a major
check on growth in the professional fraction in Figure 3,
the influx of young adults continues to be a strong force
C
C
. 1
0
C
N
preventing workforce composition from changing too rap-
idly. As can be seen in Figure 3(a), the change in pro-
fessional fraction due to young adults remains a large
negative rate throughout the simulated period of study.
The influx of young adults continues to restrain growth
in the professional fraction because there are still rel-
atively few young adults who enter the workforce with
professional skills. Even though the fraction in higher
education rises steadily over the period 1850 to 2100 in
Figure 3(a), the fraction in higher education remains
considerably below the fraction of the workforce in pro-
fessional. Because the rate of change in the profession-
al fraction due to young adults depends on the discrep-
ancy between these two fractions (the fraction of the
workforce in professional and the fraction is higher
education), the rate remains fairly steady over the en-
tire simulated period.
*When immigration rate is determined endogenously in the complete national model, the impact of falling immigration
rate will undoubtedly be more gradual. Nevertheless, the impact of changing immigration rate on workforce composi-
tion in the complete model should be similar to that discussed in this section.
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1 , 1
] JRAT10 ~ ~ ,
AKIM
L!
~
MULTIPLIER FROM CAPACITY OF
KNOWLEDGE SECTOR FOR
HIGHER EDUCATION. . . . . . . .
J ...... ?
1 1' 1
lad CAPACITY OF KNOWLEDGE ',SECTOR
FRACTIONAL DEL
FOR,HIGHER
? , .... EDUCATION ...... ,
urInr+ I
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4
a
The simulation shown in 'Figure 3 assumes an exponen-
tially increasing population and a ratio of orders for
professionals to orders for all workers (backlog ratio)
which equals the current fraction of professionals in
the workforce. Sections III.B and III.C investigate
the ramifications of more realistic patterns of popula-
tion growth and demand for professionals and labor.
III.B. Population Equilibrium
Figure 4 shows that population equilibrium acceler-
ates and prolongs the growth in the fraction of the work-
force in professional. The population input shown in
Figure 4(b) closely matches historical population in
the US to the present, and equilibrates at 260 million
in 2050. As was the case in Figure 3, the fraction of
the workforce in professional (Figure 4(a)) remains ap-
proximately constant until the flow of immigrants dimin-
ishes in 1915. However, whereas the professional frac-
tion rises to .29 at year 2100 in Figure 3, the profes-
sional fraction rises to .39 at year 2100 in Figure 4.
Comparison to Figure 3 reveals that the profes-
sional fraction rises more rapidly in Figure 4 due to
IA
It
t+1
U. N
LL.r to LP Ntn
in M M M
S t
0 1
increases in the fraction in higher education brought
about by population equilibrium. In effect, popula-
tion equilibrium removes the second major check on
growth in the professional fraction. Unlike the un-
restricted growth case, the discrepancy between the
fraction of the workforce in professional and the frac-
tion in higher education.continuously diminishes in
Figure'4(a), leading to a continuous reduction of th q
change in professional fraction due to young adults.
Consequently, the change in professional fraction due
to promotions exceeds the sum of the four negative rates
impacting the professional fraction throughout the per-
iod 1850 to 2100.
The fraction in higher education rises more rapidly
in Figure 4 than in Figure.3 because the slowdown in
population growth allows growth in capacity of the know-
ledge sector to "catch up" to growth in the demand for
higher education (Figure 4(b)). Beginning around 1915,
population (Figure 4(b)) begins its gradual approach
toward equilibrium. At the same time, the rate of growth
of demand for higher education likewise begins to slow.
(Demand for higher education is measured in people and
is formed by combining the fractional demand for higher
I" * N
S S U.
r
LL
U% UN
M n lMMu.mSmm
FRACTION OF
WORKFORCE IN
fn a rnV1 LV.rtvt?r+~ ' ,~!-. .
? ? . . ? . . . I . 1 00 ` , CHANGE IN PROFESSIONAL ~CHANGE IN
S
'ESSIONAL FRACTION IMMIGRATION FRACTION DUE TO
DUE TO UNEMPLO~fED , MOVEMENTS OF FARM
OR WORKERS TO LABOR
B
'CHANGE IN PROF'- FRACTION DUE TO Is PROFESSIONAL
f
PROFESSIONALS I 0 LA
? ` . . . . .fwa
on
? -
? ? . ~Ir . . ter`
to
olao~~gn~~
.J
N
'
U
Ui
6L
1
I 1
a
`
1.
1
0..
N
I
w
4
_
O.
.+ Q *
~-"y i'!!`r" ;._.? ~?.J~.! ?
T
`??i
In
r-
a
V
?v, l
1
I
,,~~ '
1
1
U.
18.01 '
FRACTION IN I
u
I HIGHER EDUCATION
x
1 I
M
1.
_
O C , ? ? ?
? ? ? ? ? ? , ? ? ? ? ? ? ? ? ? , ?
LL
? -
O?
O
G n
LL
I
t tH
.- ~.
I . I..
y , It~.v NV1
4f LFW
I
Ir ~NJVAto- I
401 y. -N Fp ~.~ I 1
1?r I
110
. .. . . ? . . . 1 . . . . ? . . . 1
' CHANGE IN PROFESSIONAL I
FRACTION DUE TO YOUNG ADULTS
1
, 1
I I I
? ? ? ? ? ? ? ? , ? ? ? ? ? ? ? ? + 1
0
O ?
0
O r,
V N N
Figure 4(a)
Figure 4. Behavior of Workforce Composition Model Given Population Growth and Equilibration.
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CHANGE IN PROFESSIONAL FRACTION
I DUE TO PROMOTIONS I
I 2 ??
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.?
m .,
Nm __
o
V *
UC -"an"'
R M ,.? . r r, N
C
N
0. O. t M Y 11
OD
auh+me uu
uudNNm
o a 1+,N N a Q.
?
. ? ? 1 ? ?
? d
?
?
0
00
0 x.00 1
P
1 1
MULTIPLIER FROM CAP4CITY OF
KNOWI.TEDGE SECTOR Fyn
HIGHER EDUCATION 1
HIGHER EDUCATION
w
f N N
. . ?
? N N N N N_N t IF 11 4 d ? n p N
? ?
FRACTIONAL 'DEMAND FOR
DEMAND FOR
HIGHER EDUCATION
1 ........ . . ? .
'
'
1 100 u 1
'*'~'_-CAPACIT~Y OF KNOWLEDG~ SECTOR
'
0 0
0
0
C2 0
0
0
0 N
0
U
N
?:
N
education-and the number of student-age young adults.)
Capacity of the knowledge sector (likewise measured in
people) begins to "catch up" to demand for higher edu-
cation once demand stops rising exponentially. This
occurs in the model because capacity is formulated as
a delay of demand for higher education. In real life,
such a response would occur because the current rate of
growth of capacity of higher education (buildings,
teachers, educational materials) depends upon invest-
ment,and planning decisions made on the basis of past
rates of growth in demand. Thus, once the current rate
of growth in demand slows, the rate of growth in capac-
ity continues to increase for some time.
Because both demand for higher education and capac-
ity of the knowledge sector are increasing steadily, the
"catching up" of capacity to demand is difficult to per-
ceive visually in Figure 4(b). However, the shift is.
readily apparent in the multiplier from capacity of
knowledge sector for higher education. The multiplier.
which depends on the ratio of capacity of knowledge sec-
tor to demand for higher education (called the relative
capacity of knowledge sector in Section II.B), increases
from about .67 in 1915 to about .95 by year 2100 in
Figure 4. By contrast, the multiplier from capacity of
the knowledge sector for higher education rises only to
.72 when population growth is unlimited (Figure 3(b)).
The sharp increase in the availability of higher
education (signified by the rise in the multiplier from
capacity of knowledge sector for higher education) means
that more of the young adults who seek higher education
can receive higher education. More of those who seek
higher education can recieve it because there are rela-
tively fewer young adults competing for available capac-
ity of the knowledge sector once demand stops rising ex-
ponentially. The effect of the increased availability
of higher education is a much more rapid rise in the trac-
tion of young adults in higher education
enfra Lion in
higher education rises to about .35 by 2100 4(a), as compared to .22 in Figure 3(a)) and, consequent-
ly, a greater increase in the professional fraction of
the workforce over the simulated period from 1850 to
2100.
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IMMIGRATION
CHANGE IN PROFESSIONAL
3~v / FRACTION DUE TO MOVE- I
U. N A- . TO LABOR / . . . . . . . .
a r~kalsv?masK, fllu~~ ._.~?"`'F" a ?F,,~,I v, vi~.:a~.cl u.rsar..~aa.,.arwn~ ~n
M a I 1 sau1R1.',v tar - i
e.
U. I y 1 .. gi
X 0- LL
W ~: r qi +~ - ,i .CHAt GE IN PROFESSIONAL FRACTION 1
N I Z -DUE TO YOUNG ADULTS
Response of Workforce Composition to an
Exogenous Demand for Laborers and Professionals
In Sections III.A and III.B the relative demand
for professionals and labor, represented by the backlog
ratio, equals the current fraction of the workforce in
professional throughout the simulations. Such an as-
sumption implies that the productive sectors of the
economy can absorb any ratio of professionals to labor
with no impact on promotions, unemployed professionals
to labor, or the other rates which affect workforce
composition. In order to increaSE the realism of the
analysis, Section III.C tests the response of the work-
force composition model to an external demand for a
larger fraction of professionals from 1850 to 1950
than are available and for a constant fraction of pro-
fessionals after 1950.
Figure 5 shows the response of the workforce com-
position model to a ramp input in the relative demand
for professionals and labor. The exogenous backlog
ratio begins at a value of .20 in 1850 (compared to
a professional fraction of .14) and rises steadily
d .-? Q w 1 ~` .
1- 0. h I ~~ 1 ? 1 1 1
P L! M
1 I ~?'!lame artas I 1
IP1 } 1 i~~a=~ ~ FRAC I ION IN
!~ s HIGHER EDUCATION
NAL
. . . . . . . . . .. PROFESSIO. ...
CHANGE IN PROFESSIONAL
FRACTION DUE TO
UNEMPLOYED PROF-
. ESSIONALS MOVING
I
W O d ' 1
..? w .+ O 0
.~ LL In O
lu a co
0 U.
? 1
?
o V%* 0
N N C3 .4
N
Figure 5. Behavior of=Workforce Composition Model Given an Exogenous Input
for Demand for Laborers and Professionals in the Nation.
va
O
. WORKFORCE IN
LL
Nti.+?rF Iii S.
LL Z Z X U. . m f?1 I.1
CHANGE IN PROFESSIONAL
FRACTION DUE TO ,
PROMOTIONS FRACTION OF i
until a value of .35 is reached in 1950. Backlog ratio
remains at .35 for the period 1950-2100
As can be seen in Figure 5, the ramp input In back-
log ratio means that, for the first one hundred fifty
years, a smaller fraction in professional exists than is
being ordered. During this period, production sectors
are placing a larger fraction of orders for professilpnals
than the economy can provide. Consequently, the profes-
sional fraction and the fraction in higher education
grow more rapidly in Figure 5 than in Figure 4. After
the year 2000, the professional fraction exceeds the
backlog ratio and a larger fraction of professionals
exists than is being ordered. Once the professional
fraction exceeds the fraction of professionals being
ordered, the professional. fraction adjusts to an equi-
librium value more quickly than occurs in-the preceding
simulations. A comparison of the professional fraction
in Figures 4(a) and 5(a) shows that equilibrium has not
yet been reached by the year 2100 in Figure 4(a), where-
as the professional fraction stabilizes by about 2050 in
Figure 5(a).
Figure 5 shows that the balance of forces that
eventually stabilize the simulated professional fraction
? CHANGE IN PROFESSIONAL
,),-FRACTION DUE TO
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it
o +
a.uNW
FRACTIONAL DEMAND FOR '
HIGHER- EDUCATION
.......??
HIGHER EDUCATION
_...* aua`r udr ucr--
11 G,NNNwo wo.Q. * *
woo
MULTIPLIER FROM CAPACITY OF KNOWLEDGE- SECTOR FOR
BACKIrOG' RATIO---.-
.I . . . . . . . . . ? ? ? ? ? ? ? ? 1 ? ? ? ? ? ? . ? ? 1?
? O 0
D 0
If1 O
O .r
N N N
U.
r, N
at the end of the growth cycle is fundamentally differ-
ent from the balance of forces which characterize the
-stable workforce composition during the early stages
of growth. During the period 1850 to 1900 workforce
composition in the model system remains fairly constant
as a large upward flow of laborers to professional (pro--
motions) is balanced by large influxes of immigrants and
young adult laborers. When a stable workforce composi-
tion is achieved once again around year 2050, a much
lower upward. economic flow due to promotions exists.
.The lower promotion rate is counterbalanced by (1) a
change in professional fraction due to young adults
which is much smaller than existed during the early
stages of growth and (2) by a reverse flow of unemployed
professionals to labor that is much larger than existed
during the growth phase. If the initial period of stable
workforce composition can be called.a period of high up-
ward mobility and large. influxes of new laborers, the
final steady state condition is one of low upward mobil-
ity, small influxes of new laborers, and high downward
(that is, professional-to-labor) mobility.
The simulation in Figure 5 demonstrates that, in
the absence of continuous influxes of new laborers, a
stable workforce composition can only be achieved by
creating a relatively low promotion rate and a rela-
tively high flow of professionals back to labor. As
was discussed in Sections III.A and III.B, a high pro-
motion rate can coexist with a stable workforce composi-
tion provided large numbers of new laborers are continu-
ously injected into the economy. In the absence of
large influxes of immigrant laborers or a small fraction
of young adults who enter the professional workforce, no
effective counterpressures to a high promotion rate
exist. Therefore, stabilization of workforce composi-
tion requires that promotions fall to a rate that can be
counterbalanced by the reverse flow of professionals
buck to labor.
The workforce composition model therefore illus-
trates a basic tradeoff between maintaining a high
rate of upward mobility for the icidividual laborer and
providing professional training through higher education
to large fractions of young adults. The simulation in
Figure 5 leads to a condition of high fraction in higher
education and low upward mobility. Alternatively, if
capacity of the knowledge sector were constrained,
workforce composition could stabilize at a higher
rate of upward mobility and a lower student frac-
tion. Still another alternative mix of laborer
1500
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N
a
f OD r stabilization of workforce
composition differ marked?- from the high upward economic
mobility characteristic of the early stages of national
growth.
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ISSUES UNDERLYING THE REPRESENTATION OF SOCIAL VARIABLES IN SYSTEM DYNAMICS MODELS
Dale Runge
System Dynamics Group
Alfred P. Sloan School of Management
Massachusetts Institute of Technology, Cambridge, Massachusetts
INTRODUCTION AND SU}L` ARY
Social. system simulation models are probably most
commonly criticized for "oversimplification." While re-
garded as useful for analyzing physical systems, mathe-
matical models are often considered woefully inadequate
for capturing the complexity and subtlety of human be-
havior. Such criticisms are based on the existence and
importance in social systems of such intangibles as
feelings, beliefs, attitudes, and values. This paper
aims to explore some basic issues surrounding the repre-
sentation of intangible social variables in simulation
models. Two sources of opposition to the practice of
including social variables in simulation models will
first be examined and evaluated. The reasons why in
principle social variables can be treated the same as
physical variables in system dynamics models are then
discussed. Finally, the influence of model time hori-
zon on whether a variable is treated explicitly or im-
plicitly in modeling practice is examined.
To facilitate discussion, a convenient way should
be available for referring to concepts that most people
agree are amenable to mathematization as opposed to con-
cepts whose mathematization is widely considered impos-
sible or inappropriate. The dichotomy "tangible" vs.
"intangible" is not adequate for this purpose, since,
although all feelings and beliefs are intangible, so
also are the well-mathematized concepts of force, energy,
and pressure. Force and energy are intangible, and yet
are recognized to behave in ways that can be explained
and predicted through mathematics. The dichotomy "ma-
terial" vs. "cultural" suffers from a similar weakness.
Although the term "cultural" connotes people and their
attitudes and actions, the term "material" is synonymous
with "tangible," and therefore has limited applicability.
In the absence of a more flexible dichotomy, this paper
will distinguish "physical" from "social" variables.
Although "physical" tends to imply "tangible," physical
systems are commonly thought of as a well-defined class
of systems. As a result, all the variables in physical
systems, tangible or not, will be considered physical
variables. Physical variables also include tangible
components of social systems, such as capital goods,
inventory, and population. For the intangibles of so-
cial systems, such as preferences, goals, desires, be-
liefs, attitudes, and values, the term "social" varia-
bles should suffice. Any intangible concepts that are
unique to social systems fall into the category of "so-
cial"-,variables.
The criticism referred to above about "oversimpli-
fication" in mathematical models has been especially
evident in many critiques of the recent system dynamics-
based books World Dynamics and The Limits to Growth.
The authors of Limits, for example, allegedly "ignore
the real world of social, political, and ethical values,"
and are criticized because "one of the most obvious fea-
tures of human society is that values are constantly
changing and values affect behavior."l* According to
another observer, the books "hardly concern [themselves]
with the rates of change in human habits and institu-
tions, and [they] ignore almost all of politics, econom-
ics, and the other social and behavioral sciences."2
Some of the issues raised in the above commentssnat-
urally relate to how the specific models either included
or failed to include value change. More basic issues in-
volved in any such criticism must also be addressed to
provide a context for discussing the representation of
social variables in specific system dynamics models.
Perhaps the fundamental issue is-the question whether
in principle the modeler can capture subjective social
variables and forces causing their change in terms of
mathematical models. A related question is whether so-
cial variables for which little or no data exist should
be included in mathematical models. These two issues
will be discussed in turn below.
THE POSSIBILITY OF MATHEMATIZING SOCIAL VARIABLES
Much'of the criticism of the representation of so-
cial variables in mathematical models seems to spring
from disagreement over the applicability of the scien-
tific method to the study of social systems. Whether.
the generation and testing of theories can lead to ex-
planation and prediction in social systems has been a
source of contention for many years. Recently, histor-
ians have joined in vigorous dispute over the applica-
bility of the deductive methods of the physical sciences
to the study of human society. While much of the dispute
revolves around such philosophical issues as the nature
of explanation itself,3 a large part of the concern with-
in history and other social disciplines hinges on the use
of mathematics to describe social processes. For exam-
ple, historian Stuart Bruchey argues: "to force a trans-
lation of qualitative factors into the language of num-
bers is to guide us to reality in the way of parody."4
But what is it about "the language of numbers," or mathe-
matics, that stimulates such a criticism? Indeed, the
precision and consistency of mathematics are largely re-
sponsible for the power of explanation scientists have of
physical phenomena.
Apparently, the very precision required in formulat-
ing a mathematical model is itself a source of resistance
against the practice. The ambiguity with which everyday
language describes experiences, feeling, and emotions ap-
pears related to our own experiences of the subjective
concepts being described.5 Increased precision in de-
scribing subjective matters means a greater gap between
the description itself and what is being described. For
example.-the mathematization of attitudes towards welfare
payments in no way conveys the experience of having those
attitudes. The distinction between a description of an
experience and the experience itself appears to be miss-
ing in many reactions to the objectification entailed by
using mathematics to describe subjective states of being.
According to Rudner,
The alleged failure of social science to "cap-
ture" (i.e., to reproduce or to be the psycho-
logical equivalent of) the delighted chortle of
a baby in social play with its parent, the an-
guished embarrassment of an adolescent, the nu-
ances of social interaction of a board of direc-
tors meeting or of a cocktail party, is too
often nothing but the failure to distinguish
statements and systemizing uses to which they
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may be put, from the social phenomena re-
ferred to by those statements."6 [under-
line added]
When the "statements and the systemizing uses to
which they may be put" are mathematical in nature, the
description of the experience is even further removed
from the experience itself; hence, a mistaken tendency
to reject the validity of the description. But a math-
ematical model is not supposed to reproduce the de-
scribed experience; it merely aims to describe or even
reproduce the processes by which a particular subjective
state arises and the impact of rtfht state on the rest of
the model. The main difference between a verbal and a
mathematical description is the greater precision of the
latter. The increased precision of a mathematical de-
scription does not per as mean that it cannot deal with
social concepts; there is no barrier in principle to
treating social variables the same as physical variables
.in mathematical models. A later section will explore in
some detail the similarity between physical and social
variables from the viewpoint of system dynamics
methodology.
APPROPRIATE SOURCES OF INFORMATION FOR MODELS
Even those who share the assumption of the applic-
ability of the scientific method to social systems dis-
agree over whether variables which are not quantified,
or relations between variables that cannot be tested
by statistical means, should be included in mathemat-
ical models. One end of the spectrum. of opinion is
found in econometrics, where the focus of attention is
on testing hypothesized relationships between time-
series data of measurable economic variables. More-
over, strict disciplinary bounds seem to preclude the
use of variables from fields other than economics.
Persistent efforts in the field of "behavioral econom-
ics" seem to have made little headway in introducing
new variables into traditional econometrics. For exam-
ple, the effect of consumer attitudes on economic be-
havior are claimed by econometricians to be better
explained by economic variables than by attitudinal
data.? Reports of intended investment by businesses
are found to be incorrect after the fact.8 Such in-
stances seem to validate the economist's concentration
on quantified variables in explaining economic behavior.
Criticisms of the concentration on quantified variables
can.be found within the field, however. According to
Simon Kuznets, "concentration on quantifiable factors
in formulating hypotheses may mean a definite bias in
the selection and too high a price for a statistically
testable hypothesis."9 The confinement of traditional
economics to quantifiable factors has also been criti-
cized by E. U. Phelps Brown in a presidential address
to the Royal Economic Society:
..[M]y argument implies the removal of the
traditional boundary between the subject-
matter of economics and other social
sciences....
...When the actual way in which deci-
sions are reached in the board room or across
the bargaining table has been discussed, it has
been said that economics as such has nothing to
contribute. Down with "economics as such."-LO
The viewpoint within system dynamics lies at the
opposite end of the spectrum of attitudes towards appro-
priate sources of information for mathematical models.
System dynamics shares the criticisms of confinement to
disciplinary boundary, and of exclusive consideration
of variables for which time-series data exist. For a
system dynamics model, the variables and their
interactions are specified according to their contribu-
tion to the dynamic behavior of the system in question,
not according to any disciplinary criteria. A system
dynamics model is a hypothesized set of interactions
that produces the behavior of concern. The modeler is
obliged to include all the inputs to decision processes
that can be expected to influence model behavior signif-
icantly. In-modeling economic development, for example,
this approach is especially important, since by wisde-
spread consensus, cultural, political, and social vari-
ables as well as economic variables are influential.
Including the effects of such forces does not nec-
essarily mean that the forces themselves must be made
explicit, however. Critics of World namics, for ex-
ample, often claim that attitudes and values are not
accounted for in the model. In general, variables which
adjust rapidly relative to the time horizon of a model
can be treated implicitly rather than explicitly. Con-
sequently, the price of natural resources--a social var-
iable--is not explicitly represented in the World D nam-
ics model. As resources become scarce, higher price
discourages their use. Price is an intervening variable
between availability and usage, and since price is mere-
ly a way of linking the two, an explicit treatment of
price is not necessary. The same comment applies to the
social values that impinge on birth rate. Instead of an
explicit treatment of the relevant values and the ef-
fects on those values of crowding, material standard of
living, food, and pollution, the model links those phys-
ical factors directly to the birth rate equation. The
values are by no means "ignored"; an explicit treatment
of them was simply not necessary to express their influ-
ence on the behavior of the model.
SYSTEM DYNAMICS METHODOLOGY AND SOCIAL VARIABLES
System dynamics is a methodology for understanding
the dynamic behavior of systems,- A system dynamics mod-
el contributes to a better understanding of the causes
and processes of change, and provides leverage for al-
tering the behavior of the system under study. Besides
providing a set of techniques for modeling, system dy-
namics employs a set of views about the nature of real-
world systems. This section of the paper discusses some
of those views to establish the suitability of the sys-
tem dynamics methodology for treating social variables.
Any mathematical model attempts to organize infor-
mation about real-world relationships and processes. .
The method of organization varies widely, however, from
attempts to discern correlations to attempts to estab-
lish causal relations among variables. A system dynam-
ics model is more than a collection of equations that
reproduce the time paths of system variables. System
dynamics models are meant to replicate system processes,
as opposed to the outcomes of those processes. System
dynamics models are commonly characterized as causal
models, in contrast to other types of models that ex-
press correlations between the time behavior of vari-
ables. A causal model necessarily deals with the rates
of change of system variables over time. Therefore, a
causal model can be thought of as .a set of differential
equations. System dynamics models can be described as
sets of coupled non-linear differential equations.
Another characterization of system dynamics models
appears more suited to the purposes of this paper, how-
ever. Integration is the basic dynamic process which
a system dynamics model simulates. The time behavior
of a system dynamics model is generated by integrating
the differential equations that-represent the causal
relations in the model. A principal tenet of the meth-
odology is that the process of integration in the model
is the same as integration in the.real world. In fact,,
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? K
of the two mathematical processes of differentiation and
integration, J. W. Forrester asserts that only integra-
tion occurs in the real world.11 The symbols used in
diagraming system dynamics models reflect the emphasis
on integration. The occurrence of integration is repre-
sented by a box symbol [~ called a level. The symbol
and name are intended to draw attention to the process
of integration or accumulation associated with, for ex-
ample, the phrases "level of water in the glass" or
"level of population." The level variable can be in-
creased or decreased, as, for exampe, when the level of
population is increased by birth and decreased by deaths.
The valve symbol called a rate represents actions
affecting the level variable. The rate symbol inten-
tionally connotes flow or change, while the phrase :'rate
of change" readily suggests the actions of production,
consumption, or change of attitude. A fundamental prin-
ciple of system dynamics. is that these two symbols--and
the processes they represent--are sufficient to repre-
sent the dynamics of any system.
System dynamics also stresses the phenomenon of
feedback. Feedback includes the effect that the posi-
tion of a body has on its own subsequent motion, the
effect that the size of a population has on birth rate,
and the effect that information about the size of a
firm's inventory has on its production of goods.. Feed-
back of information about the value of level variables-
the state of the system--to the rates affecting the lev-
els gives coherence to a system. Feedback gives meaning
to the term "system." Without feedback, the idea of a
system would imply no meaningful, persistent relations.
Given feedback, a boundary can be drawn around a system
and the processes and relationships endogenous to the
system (as defined by the boundary) can be analyzed.
Within the boundary chosen and over the time horizon of
interest, the process of integration and the feedback
of information are sufficient to simulate the dynamics
of any system. This generalization applies whether the
components of the system are physical, economic, demo-
graphic, social, or'psychological. -The emphasis here
is on the processes that generate system behavior, rath-
er than the context in which the processes occur. Inte-
gration and information feedback characterize all dynam-
ic systems, whether the integrated medium is energy,
houses, goods, price, or integrity.
SALES
S
WORKER
PRODUCTIVITY
NPR
NET
PRODUCTION -~ RATE
RATE*"'
ATE \X/ %
7213
INV
INVENTORY
WORKER
UCTIVITY
/ PROD
FI0..I
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The preceding discussion should make clear that the
term "model" in the system dynamics sense takes on a par-
ticular meaning. System dynamics models were earlier de-
scribed as replications of the system processes rather
than of the outcomes of those processes. A system dynam-
ics model is-actually another version of processes occur-
ring in the real world. The integrations and information
links in a system dynamics model simulate the processes
occurring in the changing real. world. From this point of
view, no important dynamics distinguish the system dynam-
ics model from the system which the model simulates.
The consonance between mathematical and real-world
systems can be seen in models of social systems. For ex-
ample, consider the interaction between inventory and
workforce in a factory. Production and hiring/layoff
policies often lead to fluctuations in the levels of in-
ventory and workforce. The basic interaction between
inventory and workforce can be summarized as follows:
an increase in factory workforce will increase the pro-
duction rate, and therefore also increase the inventory;
if inventory increases above a desired level, the work-
force will be reduced to compensate. A very simplified
version of these relationships appears in Figure 1 below.
The basic DYNAMO12 equations for the system in
Figure 1 are:
L
INV.K INV.J + DT*NPR.KK
Inventory (units)
R
NPR.KL - WF.K*WP - S
Net production rate
(units/year)
L
WF.K - WF.J + DT*NHR.JK
Workforce (persons)
R
NPR.KL (DINV - INV.K)/
Net hiring rate
(TAL*WP*TAWF)
(persons/year)
C
S -
Sales (units/year)
C
WP -
Worker productivity
(units/person-year)
C
DINV -
Desired inventory
. (units)
C
TAI
Time to adjust inventory
(years)
C
TAWF -
Time to adjust workforce
(years)
The equation for net hiring rate NHR states that, whenev-
er inventory is less than desired inventory, more persons
DESIRED
INVENTORY
DINV
'- TIME TO
/ ADJUST ,
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w
will be hired than laid off, and the size of the work-
force will grow. Workforce expands until-the discrepan-
cy between desired and actual inventory digappehrs. The
effect of increased workforce on inventory ik shown in
the equation for net production rate NPR. A larger work-
force generates higher net production; as long as work-
force grows, so does production. Workforce and produc-
tion increase until the discrepancy between desired and
actual inventory vanishes. At this point, net produc-
tion will be positive, however, and inventory will con-
tinue to grow, exceeding desired inventory. According
to the hiring equation, with inventory greater than de-
sired inventory, workers are laid off. The workforce
size thereupon begins to contract. As long as inventory
exceeds desired inventory, workforce-and consequently
net production--declines. The process continues until
inventory once again equals desired inventory, at which
point the net hiring rate goes to zero. Inventory is
falling at this point, however, and once again "over-
shoots" desired inventory. When inventory falls below
desired inventory, hiring must increase, and the entire
cycle begins again.13
The mathematical system dynamics model of the
inventory-workforce system described above produces the
same behavior as the real-world system. It does so be-
cause the mathematical model contains the same process
of integration and feedback, in the same structure rela-
tions, as the real-world system. The level variables
of inventory and cnrkforce in the example clearly arise
from the process of integration. The net accumulation
of production less sales creates inventory. Analogously,
the workforce is an accumulation of people increased by
hiring and decreased by layoffs. The integration that
occurs during computation of the level variables of the
model reproduces the same process in the real world.
The model consists of a mathematical version of struc-
ture and behavior in the actual system. Model behavior
resembles the real system because the model contains the
important real system processes.
In the inventory example, the variables were tan-
gible, and the correspondence between the model process
and real-world process was clear. The tangibility of
physical variables helps show the importance of integra-
tion in processes of change. Inventory is an accumula-
tion of the difference between production and sales;
capital stock is an accumulation of the difference be-
tween investment and discard; population is the net sum
of births and deaths. As the rates which produce accum-
ulations change in magnitude, the values of the levels
also change, but the process of integration is unchang-
ing. Beliefs, habits, and feelings can be represented
by the same dynamic process, although not so obviously.
The intangibility of these concepts prevents any visual-
ization of changes in attitudes and values in the same
manner as inventory changes, for example. The notion
that intangibles can be modeled in the same way as tan-
gible material variables is therefore commonly rejected.
Most observers posit some fundamental distinction between
physical and social variables that precludes their re-
spective treatment in parallel ways. The system dynamics
methodology, however, recognizes no fundamental distinc-
tion between tangible and intangible variables.
The distinction between physical systems, where
palpable, countable entities dominate, and social sys-
tems, where beliefs, attitudes, and values are prevalent,
must be pressed somewhat further. Consider the physical
example of a mass suspended from the ceiling by a spring,
as shown in Figure 2. The height and speed of the mass
and the compression or extension of the spring are all
apparently measurable, or at least observable. The equa-
tions of motion of the mass deal the the position of the
mass and its changes, but the integrations in the system
FIG. 2
involve kinetic and potential energies. The energies
depend on the position and velocity of the mass; for
example, a change in height is synonymous with a change
in potential energy. The dynamics of the system, how-
ever, are determined not by the height, but by the energy
change associated with a change in height. The illusory
nature of the "tangibility" of physical systems should
now be apparent. "Energy," an intangible physical vari-
able, can only be perceived through its effect on the
dynamics of the system.
The important influences on the dynamics of phys-
ical systems are less tangible than commonly realized.
The regularities of behavior in physical systems allow
the concepts of force, mass, and energy to be isolated
and interrelated in mathematical models. The regulari-
ties of social system behavior, from business cycles to
the life cycles of civilizations, suggest similar possi-
bilities for isolation and mathematization of variables
that contribute to the dynamics of systems. But a gen-
eral awareness that social variables involve the same
integration process as physical variables is lacking.
Consider, for example, the perception of poor quality
in a manufactured item, such as razor blades. If custom-
ers are used to high-quality blades, but a few poor
blades escape detection, customer opinion will start to
change. If the frequency of bad blades increases, the
customer dissatisfaction will accumulate through a pro-
cess of integration. If poor quality control persists,
dissatisfaction will begin to affect sale of the razor
blades. Here customer satisfaction--or its corollary,
dissatisfaction--is a dynamic variable, integrating the
effects of perceived blade quality to produce a change
in magnitude. It takes some time for the appearance of
bad blades to be reflected in sales, which is a further
sign that integration is occurring in the effect that
perception of poor quality has on satisfaction and pur-
chases. All integration processes introduce some delay
in a flow channel, whether of information or of matter.
The razor blade example demonstrated the process of
integration for a specific social variable. In a more
general, long-term way, the integrative nature of social
variables is revealed in the following passage:
Habits and skills accumulate in society as
in a reservoir and thus become available to
human beings in, successive generations.l4
The cumulative, or integrative, nature of all "habits,"
including modes of thought, attitudes, and values, should
be somewhat clearer from this description. This section
has attempted to establish a fundamental similarity be-
tween physical and social variables in the context of the
system dynamics methodology. As a result of this simi-
larity, there is no barrier in principle to including
both kinds of variables in system dynamics models. The
contribution to the dynamics of the system that a partic-
ular concept or variable--physical or social--is believed
to have is the key criterion for selection. To make a
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selection of variables requires a clear purpose, as well
as intimate familiarity with the system being modeled.
The next section will illustrate some of the,influences
that model purpose has on the treatment of social
variables.
IMPLICATIONS FOR MODELING PRACTICE
The previous section attempted to establish that,
in principle, social variables can be included in a sys-
tem dynamics model. Physical and social variables can
be treated analogously because each,involves integtation
and feedback. However, the selection of variables,
physical and social, to include as integrations in a
model is determined by the purpdses of the model. The
behavior modes which'the model is intended to reproduce,
and the policies which the model will test, govern the
composition of a model's variables. The influence of
model purpose on model composition is easy to assert,
but quite another matter to-apply effectively in prac-
tice. This section will illustrate the influence of
model time horizon (which depends on purpose) on whether
a given social variable is treated implicitly as a pa-
rameter or explicitly as a dynamic variable--that is, an
integration.
Consider the relationship between two variables, A
and B, given by the equation
Here A and B might represent quantities that change over
time, such as inventory, price, razor blade quality, or
customer satisfaction. Equation (1) states that when
there is a change in variable B, variable A changes im-
mediately to a new value. Let us look closer at this
statement. In principle, variable A cannot change imme-
diately in response to a new value of variable B. Some
amount of time is required for the information about the
new value of B to be transmitted. Some dynamic process
must underlie the adjustment of variable A to its new
value. The dynamic process underlying Equation (1)
might be like that represented below in Figure 3. The
rate of change of variable A in Figure 3 is given by:
A - (k'B - A)/T
(2)
If A - k?B in Equation (2), the rate of change of A.
or
A, will be zero. Therefore, as long as B remains un-
changed, Equation (1l holds true. Given, say, a one-
time increase in B. A will act to bring A back into
equality with k?B, at which point A will once again be
zero. Over some period, however, Equation (1) will
not hold true.- The length of the period of inequality
depends on T, the time constant of adjustment in Equa-
tion (2). The time constant in a measure-of the speed
of adjustment of A to a new value of B. The smaller the
time constant, the faster A equilibrates A with B, and
vice versa.
In other words, an apparently static relationship
between variables (provided the relationship is not an
identity) actually embodies an assumption about the
dynamics of that relationship. Specifically, the time
constant of adjustment--relative to other time constants
in the system--is so short that the relationship between
the two can be approximated as static. In other words,
relative to the other dynamic processes in.the system,
the-two variables can be considered to be in equilibrium
with each other. The relative lengths of the time con-
stants in a system play a large role in determining the
need for an integration to represent a given variable.
If the time constant T in Equation (2) is sufficiently
short, the value of A at any time can be approximated by
knowing the value of variable B and of the parameter k.
Even though the value of A can vary, only the values of
the parameter k and variable B must be known to deter-
mine A. A need not be treated as a separate level, or
integration.
The particular nature of the modeled system will
greatly influence whether variables--physical or social
--must be introduced explicitly in the model as inte-
grations, or treated implicitly by parameters. Consider
the razor blade example once more. The time constant of
change for the level of customer satisfaction determines
whether customer satisfaction must be treated explicitly
as an integration, or implicitly by using a parameter in
the feedback loop between blade quality and rate of
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sales of razor blades.* The relative time constants of.
the other state variables will determine'the choice.
If the time constant of a variable is very short
relative to the model time horizon, the variable can be
represented implicitly. On the other hand, a variable
may change so slowly that it can be approximated as a
constant. Holding some variables constant in a model is
a useful practice; the dynamic structure needed to gen-
erate those variables can be omitted. Therefore, atten-
tion can be focused on important elements of the problem
that change within the model tiAhe frame. To address is-
sues that evolve over longer time horizons, however,
more and more constants must be expressed as variables-.
As the model time horizon is extended, only those rela-
tively basic aspects of the physical or social state of
the system can be assumed to be constant. In principle,
the modeler should be able to bring parameters into the
..model as variables as the time horizon extends, until
only a fairly small set of basic human values and phys-
ical relations need be held constant. At the extreme,
human values are likely to resemble basic needs more
closely, with very long time constants-that is, which
change very little if at all.
The extent to which changes in any variable--phys-
ical or social--must be treated in a model depends on
the time horizon of the model. For short-term studies
of trade cycles, population can be treated as constant.
Similarly, resource availability can be assumed constant
over short time spans. The same general idea applies to
social variables also. Attitudes toward birth control
can be assumed constant over a short time span; the
public pressure for increasing welfare is constant over
short time spans. To omit variables or treat them as
constants in a given model structure in no way implies
any diminution of the importance of those variables. It
merely reflects a pragmatic approximation, based on rel-
ative time constants for the changes in variables--
always relative to the time horizon of the model.
Because the importance of time constants is a relative
matter, the example in Figure 3 of the relationship
A - k?B can be looked at in another way. If the time
horizon of the study is in the range of the time con-
stant T for variable A, attention could focus on the
details of the change process of variable A. If var-
iable B changes very slowly over this time horizion,
variable B could be treated as a constant in the equa-
tion for the rate of change of variable A.
Another illustration should help to clarify this
point. We will consider the impact of desired inventory
on production rate. In Figure 4, inventory INV should
be conceived as a physical integration, such as goods or
people. Even though INV is a physical variable, desired
inventory DINV is a social variable. The social var-
iable DINV forms part of the policy for the production
of the items in INV, as shown in the equation for the
production rate;
P - (DINV - INV)/TAI ? (3)
For short time spans, DINV is surely constant, as shown
here. Suppose DINV equals 1000 units. This target may
be constant over a few days, weeks, or even months, but
production policy is unlikely to be independent of sales;
if the sales rate varies, as during growth, or Aver the
.course of the business cycle, the value of DINV is sure
to change. DINV may also change, for example, if the
TIME TO
ADJUST
INVENTORY
TAI
00,
average sales rate does not change, but the variance in
sales increases. If the time horizon for the model is
going to include periods of varying sales, the constant
DINV must come within the boundary of the model as a
variable. The amount of desired inventory usually re-
flects a desire to meet a constant sales rate for some
length of time. In other words, DINV is the number of
units in stock required to meet constant sales for a
certain period of time if production were zero (See Fig-
ure 5).
In Figure 5, average sales AS is an exponential
average of the sales rate S. Time is required to aver-
age the instantaneous sales rate; consequently, AS is
generated by an integration process, and is shown as a
level variable in Figure 5. Desired inventory DINV is
now a variable, as given by the equation
DINV - ICT*AS (4)
Note that Equation (4) has the same form as Equation (1).
The form of this equation presumes that the adjustment of
DINV to a new value, when AS changes, takes place rapidly
relative to the other changes in the system.
In the present formulation, desired inventory has
become ' a. variable within the model to account for the
effects that variable demand might have on production
policies. Therefore, a new parameter, inventory cover-
age time ICT, was required. The value of DINV is always
known if the variable AS and the parameter ICT are known.
To take the example a step further, the value of ICT is
not a magical number. Why, for example, should a firm
hold inventory in the amount of two months of sales rath-
er than three or even ten? The value of inventory cover-
age itself reflects a balance between the desire to sat-
isfy customers and the costs entailed by carrying high
inventory. Company traditions can also be expected to
play a significant role. The effect of inventory cover-
age time ICT on customer satisfaction can be seen in the
following way. Equation (4) can be rewritten as ICT
DINV/AS. Here ICT is the ratio of desired inventory to
*Instead of a single parameter, several parameters may be used to ekpress a non-linear relation between blade qual-
ity and sales. In either case, customer satisfaction is only implicitly present, since its effect on sales is giv-
en by the values of blade quality and of the parameter(s).
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TIME. i-0
ADJUST
INVENTORY
average sales. The higher the value of ICT, the great-
er is inventory relative to sales. The ratio of desired
inventory to average sales affects the speed with which
a given customer order is shipped. Therefore, the value
of ICT implicitly measures the fraction of demand that
can be satisfied directly from inventory, and thereby
affects the average delivery delay to the customer.
The effect of ICT on costs is apparent; a higher value
of ICT means more inventory on hand at any given time.
Carrying inventory costs money; this cost also affects
the actual value of ICT. Traditions within the firm
influence the extent to which pressure from consumer
satisfaction and inventory carrying costs are converted
into a change in inventory coverage time. In this man-
ner, inventory coverage time ICT can be brought within
the model boundary as a variable. In doing so, other
parameters are likely to be necessary; depending as al-
ways on model purpose, these parameters can in turn be
incorporated into the model as variables. As the time
horizon of interest extends, only those variables that
are relatively unchanging relevant to the problem can
safely be-treated as parameters.
AS
AVERAGE SALES
CONCLUSIONS
In principle, no barrier constrains the incorporation
of social variables in mathematical simulation models.
Much of the'resistance to doing so arises from the preci-
sion with which such models deal with intangible, subjec-
tive concepts, and Pram a failure to distinguish the de-
scription of a concept from the concept itself. Moreover,
social variables can and must be included in a model, even
in the absence of statistical data for the variables.
Social-variables can be treated the same as physical
variables in system dynamics models. Both types of var--
tables invdlve the process of integration and the phenom-
enon of information feedback. With respect to modeling
practice, the purpose of the model governs whether and
how both physical and social variables are incorporated.
Model time horizon, and the relative time constants for
processes within the system, are especially important in
determining whether variables are treated explicitly as
state variables, implicitly by means of parameters, or
are assumed constant.
NOTES AND REFERENCES
1H. S. D. Cole, et. al., Models of Doom (New York: Universe Books, '1973), p. 202.
2K. Deutsch, "Quantitative Approaches to Political Analysis: Some Past Trends and Future Prospects," in Mathe-
matical Approaches to Politics, Alker, Deutsch, and Stoetzel, eds. (Amsterdam: Elsevier, 1973), p. 58.
3See, for example, W. Dray, "Explaining What' in History," in Readings in the Philosophy of the Social Sci-
ences, H. Brodbeck, ed. (London: Macmillan, 1968), p. 343.
4S. Bruchey, The Roots of American Economic Growth, 1607-1861 (New York: Harper & Row, 1965), p. 10.
5For an example of the difficulty in dealing with the ambiguities of the term "values," see a discussion of its
varying definitions in M. Rokeach, The Nature of Human Values (New York: The Free Press, 1973), pp. 3-25.
6R. Rudner, Philosophy of Social Science (Englewood Cliffs, N.J.: Prentice-Hall,1966), p. 69.
7x. Evans, Macroeconomic Activion Theory, Forecastine. BIId Control (New Yorkt Harper & Row, 1969),
pp. 461-466.
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44
8See, for example, F. Modigliani and 0. Sauerlender, "Economic Expectations and Plans of Firms in Relation to
Short-Term Forecasting," in Short-Term Economiie,Forecastin&, L. Klein, ed. (Princeton: Princeton University Press,
1955), p. 261.
9Quoted in Bruchey, op. cit., p. 6.
10E. H. Phelps Brown, "The Underdevelopment of Economics," in The Economic Journal (March 1972), p. 7.
11J. W. Forrester, Principles of Systems (Cambridge: Wright-Allen Press, 1968), pp. 6-11 - 6-12.
12DYNAMO is a computer languae commonly used for system dynamics models; see J.,Pugh, DYNAMO II User's Manual
(Cambridge: MIT Press, 1973).
13A full discussion of the behavior of this system tan be found in N. Mass and P. Senge, "Understanding Oscil-
lations in Simple Systems," System Dynamics Group Memo D-2045-1, August 1, 1974, MIT, Cambridge, Massachusetts.
14R. Dubos, So Human an Animal (New York: Scribners, 1968), p. 40.
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CONSTRUCTION AND TESTING OF THE NATIONAL SOCIO-ECONOMIC MODEL:
FQUAfTIONS FOR CORPORATE FINANCE
Alan K. Graham*
System Dynamics Group
Alfred P. Sloan School of Management
Maseechusetta.Institute of Technology, Cambridge, Massachusetts
The System Dynamics Group at MIT is constructing a
simulation model of the US economy. The national socio-
economic model addresses a wide Spectrum of social and
economic problems, ranging from business cycles and in-
flation to long-term economic growth and resource deple-
tion. Consequently, the model structure is quite exten-
rive. In fact, the national model is too large to be
constructed and tested in a purely ad hoc fashion. This
paper discusses orderly, step-by-step procedures, both
in the abstract and for the specific example of equa-
tions representing corporate finance. Rather than fo-
cusing on technical details, this paper emphasizes the
larger issues which motivate the choice of procedures
for model construction and testing.
sector depicts the purchasing, borrowing, and savings
decisions of households, as well as workforce partici-
pation. The demographic sector determines births,
deaths, population age distribution, and levels of edu-
cational attainment. The labor sector represents inter-
industry labor mobility. Finally, the production sector
depicts corporate and other commercial activities.
The production sector describes production, order-
ing of capital and other factors of production, hiring
and firing, price setting, borrowing, and payments.
The finance equations depict the three latter activities
--pricing, borrowing, and paying, as well as accounting,
profitability, and the impact of financial considerations
upon inventory ordering and hiring.# The finance equa-
tions assume a major role in several of the problems to
be addressed by the national socio-economic model. In-
flation by definition arises from increases in the
prices of sector outputs. Financial constraints prob-
ably diminish the rate at which production can be in-
creased during the upswings of the four-, twenty-, and
fifty-year business cycles. However, the delays inher-
ent in planning and financing new investment may in fact
cause overshoots and contribute to cyclical behavior.
Finally, the financial equations depict the channel
through which monetary policies influence the real
economy. .
The national socio-economic model addresses itself
to a variety of problems encompassing a variety of time
horizons.** The national model contains enough short-
term detail to analyze the four-year business cycle and
various types of inflation.*** Over longer time-spans,
the national model depicts the underlying causes of the
twenty-.and fifty-year cycles of economic development
(the "Ku?,nets cycle" and the "Kondratieff cycle," respec-
tively). Finally, the model incorporates sufficient de-
to depict the national "life cycle" of economic develop-
ment, growth, and eventual resource depletion.****
To organize the myriad details of so comprehensive
a model, the national socio-economic model is divided
into six sectors: the government, financial, household,
demographic, labor, and production sectors.+ The
government sector represents taxation, fiscal policy,
and formulation of support programs such as social se-
curity and unemployment insurance. The financial sec-
tor represents the spectrum of financial institutions,
including the Federal Reserve System. The household
One must understand a model to use if effectively.
The ultimate purpose of a model is to aid in designing
and evaluating policies which improve the behavior of the
system. To find such policies, model behavior, and the
feedback loops which generate the behavior, must be well-
understood. Also, a thorough understanding of model
structure is necessary to translate simulation results
into statements about policy alternatives in the real
system: Policy analysis with a model indicates the
changes which improve the behavior of the system. But
*Research on the National Soc.io-Economic Model is funded by the Rockefeller Brothers Fund. The Author is a
National Science Foundation fellow.
**A more thorough discussion of the issues addressed by the national socio-economic model appears in Jay W.
Forrester, "Understanding Social and Economic Change in the United States" (Proceedings of the Summer Computer
Simulation Conference, San Francisco, Calif., 1975).
***Fragments of the national model have been used to investigate business cycle behavior. A brief discussion ap-
pears in Nathaniel J. Mass, "The Dynamics of Economic Fluctuations: A Framework for Analysis and Policy Design"
(Proceedings of the Summer Computer Simulation Conference, San Francisco, Calif., 1975). For more details, see
Nathaniel J. Mass, Economic Cycles: An Analysis of Underlying Causes, Wright-Allen Press, Cambridge, Ma., 1975.
****A preliminary study of long-term national economic development is Nathan B. Forrester, The Life Cycle of Nation-
al Economic Development, Wright-Allen Press, Cambridge, Ma., 1974.
4-A more extensive summary of the organization of-the national model is Gilbert W. Low, "The National Socio-
Economic Model--An Overview of Structure" (System Dynamics Group Memorandum D-2123).
to more detailed description of the finance equations appears in Nathaniel J. Mass, "The Production Sector of
the National Socio-Economic Model--An Overview" (System Dynamics Group Memorandum D-2143).
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effective action cannot be taken without knowledge of
the real processes to which the model changes
correspond;* .
Unfortunately, the behavior of a model with the
complexity of the national socio-economic model almost
defies understanding. Completed versions of the nation-
al model.will contain literally thousands of feedback
loops. The task of attributing the various model be-
havior modes to the individual structural elements of
the model is formidable. Many realtionships in the
model are nonlinear. Among othtf problems, nonlinearity
allows.a single behavior mode to be caused by-any one of
several independent causes, depending on conditions in
the rest of the model. For example, an inflationary
spiral can be instigated by persistent monetary overex-
pansion, monopolies in key industries, rigidities in
the labor market, rising expectations of standard of
living, high interest (or dividend) costs, or disloca-
tion resulting from attempts at wage and price control.
Consequently, nonlinearities allow the national model to
generate extremely complex behavior modes. Finally and
perhaps most' seriously, complex models such as the na-
tional model are in general counterintuitive. That is,
the parameters which can significantly alter model be-
havior are not the obvious ones.**
To understand a model as complex as the national
model, one can only proceed in a step-by-step manner.
The national model is too complex to analyze as a single
unit. In fact, many of the individual sectors, espe-
cially the production sector, appear to be too complex
to analyze as a single unit. However, a fairly small
group of equations within a sector does comprise a prac-
tical beginning-point for model analysis. Even a small
group of equations exhibits several behavior modes and
responses to exogenous inputs. If the group of equa-
tions forms more than one feedback loop, the modeler can
distinguish the dominant feedback loops essential to the
model behavior from the less-important loops. The mod-
eler can also identify sensitive and insensitive param-
eter variations--changes in parameter values which
either do or do not alter the model behavior.
After the modeler analyzes two or three small
groups of equations, the groups can be combined to form
a larger unit for further analysis. The interactions
between the equation groups may give rise to new be-
havior modes, not exhibited by the individual equation
groups. The connections between the equation groups
form new feedback loops, which may (or may not) dominate
the loops within the individual equation groups. The
new feedback loops may also alter the sensitivity of
model behavior to parameter changes. Based on know-
ledge of the smaller units, then, the modeler can ana-
lyze the new behavior modes, dominant loops, and param-
eter sensitivities of the larger unit in a fairly
straightforward, step-by-step fashion.
C. Construction of Models
The system dynamics literature may give the impres-
sion that simulation models are initially created in
their final, fully-developed form. In fact, most pub-
lished models result from a fairly long and involved de-
velopment. Most initial models contain "bugs." Elim-
ination of typing errors and careless errors such as
sign inversions only begins the debugging process.
Simulation usually uncovers deficiencies in the formu-
lation of the model equations. Closer scrutiny reveals
that equations which initially seemed adequate in fact
give responses of unrealistic magnitude or timing.
Variables sometimes even move in unrealistic directions
in response to unforeseen combinations of inputs.
A model usually requires a significant amount of test-
ing and reformulation before each equation gives a con-
sistently realistic response, even under a variety of
extreme conditions.
A model with the complexity of the national socio-
economic model is virtually impossible and quite expen-
sive to debug as a single unit. Such a model contains
thousands of feedback loops, so a defective equation
may give rise to unrealistic behavior in many different
and widely separated parts of the model.' Therefore,
beginning with unrealistic behavior and tracing the path
back to the defective equation(s) poses great difficul-
ties. More insidiously, the national socio-economic
model represents decisions and the adaptation of
decision-makers to changing circumstances. The parts
of the model which interact with a defective equation
sometimes adaptively counteract the unrealistic responses
of the defective equation. Until a very detailed exami-
nation is made, such adaptations may completely mask the
symptoms of the defect.
A practical debugging method is to begin with small
groups of equations. After obtaining successful compi-
lations,etest the behavior. To test the behavior, the
variables defined outside a given set of equations must
be initially held constant. Therefore, feedback loops
which affect behavior in the real system may not operate
during the initial tests. Given the possible absence of
feedback loops, however, the behavior should be plausible.
If not, determine the formulation changes necessary to
make the.behavior plausible, given the constraints of the
testing procedure. When tests finally yield plausible
behavior.by the initial groups of equations, combine
them into larger units. The new behavior modes of the
larger unit may expose other equations in need of reform-
ulation. Repeat the cycle of testing and reformulating,
until the resulting behavior is plausible and still larg-
er units of equations can be formed. In this way, con-
struction of even large, complex models can proceed in
an organized and efficient fashion.
D. Validation of Models
In the most general sense, validation is any proce-
dure which increases confidence in the utility of a mod-
six considerations apply to both model equations and
model behavior.+
Purpose. Are the model structure and the model be-
havior consonant with the overall model purpose? Does
*An excellent example of this "translation" of model behavior appears in Chapter 7, "Interpretations" in Jay W.
gorrester, Urban.Dynamics MIT Press, Cambridge, Ma., 1969.
**To be exact, the counterintuitive nature of social systems and models of social systems characterizes not the sys-
tems themselves, but our understanding of those system. The properties of complex systems which render them coun-
terintuitive are discussed in Chapter 6, "Notes on Complex Systems" in Urban Dynamics, p. cit.
4A more extensive discussion of model validity appears in Jay W. Forrester, Industrial Dynamics, MIT Press, Cam-
bridge, Ma., 1961, pp. 115-129.
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the model explain the causes'of the problem being ana-
lyzed?. Does the model contain enough etructpre to per-
mit analysis of the effects of policy intervention? If
not, the model has little validity as a policy-making
tool.
Perceptions. Do the model structure and behavior
match the perceptions of people who work within the real
system? Is the model response to exogenous inputs, pa-
rameter changes, and policy changes plausible? Do the
cause-and-effect relationships in the model structure
correspond to perceived cause-and-effect relationships
in the real system? The equation9 in the production
sector, for example, should represent investment deci- -
sions in a form which corporate executives could recog-
nize as being similar to the real investment decision.
process. The information flows in the model should
represent only the information streams actually avail-
able to real decision-makers. Similarly, a corporate
executive should not be able to readily distinguish the
behavior of the production sector (with suitable inputs)
from behavior of real corporations or sectors.
Extremes. Do the individual model equations and
the whole model respond in a realistic, plausible manner
to extreme conditions? Certainly, evaluating the model
under conditions approximating the historical values
can to some extent test the validity of the model. How-
ever, extreme conditions constitute a more difficult and
hence more' discriminating validity test. Suppose, for
example, that the national model fails to behave plausi-
bly under wage and price controls; the model must lack
an element of real-world structure which can potentially
assume major importance.
Generalit. Does resetting the parameters allow
the model to represent a variety of cases and historical
examples? Generality is especially important in the na-
tional socio-economic model, where one set of equations
depicts a variety of industrial sectors. The pricing
equations, for example, should be able to represent ei-
ther an auction-type market for commodities, where sup-
ply and demand determine price, or a cost-plus market,
where prices are determined principally by corporate
profitability, or any cases in between these two
extremes.
Replication of Data. Can the model parameters be
set to replicate in some sense the available statistics?
The replication can be judged either by inspection of
data, or by more formal statistical techniques. Inspec-
tion of data on the business cycle, for example, can in-
dicate typical magnitudes of variables, the typical per-
iod of each cycle, and the timing of events within each
cycle. A model of business cycles should replicate
these features of the data.
Discovery. Do the model equations or the model be-
havior engender new observations about the real system?
Does the model predict behavior modes which are subse-
quently observed in the real system?
These six validity criteria are applicable to every
stage of model construction. Section II.A discusses in
more detail the evaluation of individual equations with
respect to purpose, perceptions, extremes, generality,
replication of data, and discovery. Similarly, behavior
of pieces of a model, and behavior of the whole model
can be tested for validity using the same six criteria,
E. Model Construction and Testing
Model construction proceeds with alternate formula-
tion and testing of pieces of the model, while the size
of the pieces gradually increases. Validity tests are
performed both on the model equations as they are formu-
lated, and on the model behavior during the model con-
struction. Model testing also forms the basis for under-
standing the model behavior, which makes possible subse-
quent policy design. In short, constructing, validating,
and understanding a model are concurrent processes. When
each portion of the model is constructed, it should also
be tested for validity, and analyzed to find the underly
ing causes of the behavior.
The structure, validity, and policy implications of
the national socio-economic model emerge quite slowly, as
the step-by-step process of model-building proceeds.
Models smaller and less complex than the national model
can be constructed, validated, and used as policy tools
as single entities, without the need for gradual con-
struction. Smaller, less complex models possess only one
or two behavior modes, and therefore can be presented and
analyzed as a single entity. The national model differs
sharply. The completed model will encompass thousands of
feedback loops, and exhibit literally dozens of behavior
modes. Each behavior mode will result from a unique set
of important feedback loops. The only workable format
for communicating the structure, behavior, and policy im-
plications of such a model is to document the intermedi-
ate steps in the process of model construction. Descrip-
tions of intermediate steps are already available for cy-
clic behavior in the production sectors of the national
model, and for the portion of the financial sector de-
scribing monetary policy formulation.* The following
section discusses the process of constructing and testing
of another component of the national model, the equations
which describe corporate finance.
II. AN EXAMPLE: EQUATIONS FOR CORPORATE FINANCE
Section II illustrates equation formulation, valid-
ity testing, and behavior analysis by discussing these
procedures for the financing equations in the national
model. For each production sector, these equations de-
scribe payments, borrowing, accounting, product pricing,
and the impact of financial considerations on investment
and inventory planning. The discussion does not focus
on the mechanics of testing. Instead, the emphasis is
on the'motivations for performing each separate test,
and on the use of test results in understanding the na-
tional economy. In conformance to the previous section,
the discussion begins with the simplest units for anal-
ysis, the individual equations. The discussion then
progresses to procedures for constructing and testing
single- and double-sector models.
*Mass, Economic Cycles, op.'cit., and W. W. Behrens III, "A Policy Structure for Monetary Control Decisions,"
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A. Equation Formulation
A relatively small group of equations-cap be clear-
ly and thoroughly discussed, especially with respect to
the validity testing of the equations. Indeed, the pau-
city of discussion on validity seems to underlie the
critical reception of World Dynamics and The Limits to
Growth.* A thorough and convincing presentation of mod-
el structure must necessarily contain enough information
to evaluate the validity of the model structure. The
general guidelines for validity testing in Section I.D
provide a convenient framework for presenting the fi-
nance equations.
Purpose. How do the equations relate to the ovei-
all purpose of the model? In which behavior modes do
the equations play a significant role? Is the level of
detail appropriate for the model purpose?
Perceptions. What real-world phenomena does each
equation represent? How are the equations consistent
with descriptive, theoretic, and quantitative know-
ledge? The description of the equations should make
sense to a person familiar with real corporate finance.
The equation description should also relate the model
structure to the appropriate economic theory.
Extremes. How do the equations respond to extreme
conditions, and is the response plausible? For example,
suppose the model equations indicate that very high in-
terest rates cause diminution of bank borrowing and
stock issue. A thorough equation description would re-
late this diminution to a discussion, from a managerial
viewpoint, on investment planning and alternative means
of obtaining funds.
Generality. Does resetting the parameter values
allow the finance equations to represent the variety of
characteristics of the real economic sectors? For exam-
ple, the household sectors in the national model will
utilize the finance equations of the production sector;
the finance equations must therefore depict not only
corporate financing, but also household financing. The
equation descriptions should indicate how different fi-
nancing characteristics, such as risk factors and bor-
rowing habits, are reflected by parameter variations.
Replication of Data. Each equation defines an out-
put variable in terms of one or more input variables.
Cross-sectional or time-series data is often available
for both input and output variables. Each equation
should in some sense replicate that data. Replication
is fairly straightforward to test for equations with one
input variable: For known values of the input variable,
does the equation give an appropriate value of the out-
put variable? Testing replication of data for equations
with more than one input variable, however, requires
considerable care, due to potential statistical
problems.**.
Discovery. Do the. equations specify relationships
which are not usually considered? The formulation of
new relationships frequently arises from consideration
of extreme conditions. For example, Urban Dynamics
posits a relationship which restricts migration into a
city when the city's housing stock is already over-
crowded.-F Historically, this relationship has'not been
critical to urban behavior. Yet this relationship is
central to the policy recommendation.' A realistic
model should not depict only those relationships which
have been important in the past. A realistic model
should also depict relationships which potentially as-
sume major importance under conditions substantially
different from the past.
Two goals motivate the testing of the finance equa-
tions within a single production sector: validation and
understanding. Showing that the model behavior is plau-
sible and realistic, even under extreme conditions, en-
hances the validity of the model. Understanding the
role of the finance equations in the dynamics of the
single sector establishes a groundwork for analyzing
the interactions between the real and money sectors of
the. economy. The discussion below identifies several
specific instances of the effect of financial variables
upon productive activity.
Behavior testing begins with tests on the finance
equations in isolation. Writing the equations in a com-
pletely separate model, however, requires too much ef-
fort. A more efficient method of testing involves writ-
ing the equations for the entire production sector, but
setting parameters to immobilize selected parts of the
sector. Setting parameters to maintain inventories and
production at constant values in effect allows testing
the finance equations in isolation.
*Jay W. Forrester, World Dynamics, Wright-Allen Press, Cambridge, Ma., 1971, and Dennis L. Meadows et al., The Lim-
its to Growth, Potomac-Associates, Washington, D.C., 1972. A discussion of the misconceptions engendered by these -
relatively short presentations appears in Jay W. Forrester, Nathaniel J. Mass, and Gilbert W. Low, The Debate on
World Dynamics: A Response to Nordhaus," Policy Sciences 5: pp. 169-190, June, 1974. In contrast to the shorter
presentations, the much more thorough report on the same subject matter has been received virtually without com-
ment (Dennis L. Meadows et al., Dynamics of Growth in a Finite World., Wright-Allen Press, Cambridge, Ma., 1974).
**Within a dynamic feedback system, variables are commonly highly correlated. Causality is accordingly difficult to
infer in an equation with multiple inputs: If several input variables vary at once, changes in the output cannot
be easily attributed to any single variable. Forrester, Low, and Mass (on. cit., pp. 171-177) give an example in
which the correlation between an input and an output :variable indicates the-opposite of the true structural rela-
tionship. The statistical problems can seemingly be overcome by formal estimation procedures. However, these
procedures are also vulnerable to considerable error; see Peter M. Senge, "An Experimental Evaluation of General-
ised Least Squares Estimation," System Dynamics Group Working Paper D-1944-6.
4For more extensive discussion, see Alexander C. Makowski, "Housing and Migration in Urban Dynamics," in Walter W.
Schroeder III, Robert E. Sweeney, and Louis E. Alfeld, eds., Readings in Urban Dynamics, vol. II, Wright-Allen
Press, Cambridge, Ma., 1975, Reading 4.
Urban Dynamics, op. cit., Chapter 5, "Urban Revival."
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Validity testing focuses on examining the plausi-
bility of model behavior, even under extreme-conditions.
Even when the production rate and inventories are held
constant, the financing equations can respond to inputs
by varying payment schedules, borrowing, wages and
prices, and ultimately defaults. Thus, the single-
sector model should yield moderately plausible responses,
even to extreme values of interest rates, loan avail-
ability, wage demands, or cost increases.
Model testing should also be used to enhance the
understanding of the model's dynamics. Tests can indi-
cate which loops in the model are important to its
short-run and long-run behavior. Knowledge of the
model's dominant loops in turn reveals potentially
sensitive parameters. Most importantly, however,
model tests evaluate behavior modes of the individual
unit being tested which are important to the dynamics
of the entire model. For example, a variety of theories
exist which explain how and why a recession becomes a
depression. One hypothesis is that depressions result
when a downturn progresses to the point where business
failures and the resulting defaults put a significant
strain on the econo;ny as a whole. A critical feature
of this hypothesis is the existence of a "chain reac-
tion" of business failures, where financial difficulties
in one sector cause it.to default on accounts payable,
which in turn engenders financial difficulties in other
sectors.
One important set of tests, therefore is to deter-
mine the parameter values and internal financial condi-
tions for which defaults on accounts receivable can
cause comparable defaults on accounts payable. In other
words, the tests define the circumstances in which busi-
ness failues can propagate throughout the economy in a
"chain reaction." If the tests reveal that the "chain
reaction" can occur only in absurd circumstances, then
the investigator must look elsewhere for an explanation
of depressions. But if the tests indicate that a "chain
reaction" can occur under plausible circumstances, the
tests provide both a basis for further investigation,
and a preliminary set of economic indicators which, at
least on the model, indicate vulnerability to "chain
reactions" of business failures.
The next stage in single-sector behavior testing
allows the production rate.and the.ordering and inventor-
ies of'factors of production to vary, but maintains the
fixed endogenous inputs such as orders for finished pro-
ducts, interest rates, and delivery delays. Before go-
ing on to evaluate new dynamic hypotheses, the results
of the previous testing should be tested in the new mod-
el (or more precisely, in the same model with parameters
which activate previously immobilized equations). New
feedback loops are activated which may alter loop domi-
nance and parameter sensitivity. For example, a tight
.cash position reduces inventory ordering and accounts
payable, which can somewhat alleviate the tight cash
position. This feedback loop, by further cushioning
the sector's cash balances, may. reduce the importance
of other loops which control cash balances. Also, the
new feedback loop may alter the circumstances in which
a "chain reaction" of business failures can occur.
Freeing the production rate allows the sector to
experience four-year and twenty-year business cycles.
From the viewpoint of monetary policy formulation, it
is important to know the extent to which financial var-
iables influence business cycles. Monetary policy does
influence the production sector. However, the sector
attempts to counteract the influence of restrictive
monetary policies by delaying payments of accounts pay-
able, borrowing despite high costs, raising prices, or
cutting costs. Suppose sudden changes in interest rates
cannot initiate business cycles due to cushioning by the
negative feedback loops in the financial sector. Then
a rapidly-changing monetary policy probably cannot ef-
fectively counteract business cycles, either. The re-
sponse of the single sector to interest changes there-
fore assumes major importance to policy-makers.
The effect of financial variables on business cycles
is of interest in economic theory. Prewar and postwar
business cycles exhibit different turning points, damp-
ing, and period; many of the differences may be due to
the different interest rates and monetary conditions be-
fore and after the way. Since postwar interest and div-
idend payments in general comprise a larger share of a
firm's total revenues, rapid expansion should be more
difficult to finance than during the prewar period.
This lessened ability to expand might account for the
smaller amplitude of the average postwar business cycle.
This hypothesis is easily tested by examining a single
sector's cyclical behavior under constant easy money
conditions and under constant tight money conditions.
Single-sector testing also forms a basis for under-
standing inflation. While inflation obviously does not
arise exclusively from corporate actions, the response
of sector prices to various sector inputs obviously
forms a critical link in the overall structure respon-
sible for inflation. For example, consider the sector's
response to factor cost increases. To the extent that
either other factors can be substituted for a costly
factor, or costs can be temporarily met through borrow-
ing, increasing factor costs will not be passed on to
prices. If the substitution takes several years and
borrowing is impractical, however, prices must increase
in the interim to cover costs.
The effectiveness of anti-inflationary policies de-
pends critically upon the promptness with which each pro-
duction sector passes on cost increases as price in-
creases. If the production sectors pass on cost in-
creases only slowly, the wage- (or cost-) price spiral
cannot persist independent of "outside" causes of infla-
tion such as oil price increases and government deficit
spending. If so, inflation can be controlled by control-
ling the "outside" causes of inflation. If the produc-
tion sectors pass on cost increases quickly, the wage-
price spiral can persist for some time, even in the ab-
sence of "ogtside" price stimuli. In this case, infla-
tion can only be controlled by some means which restrains
price rises in each sector.*
Single-sector testing can indicate the extent to.
which inflation arises from economic change or disloca-
tions. In a corporate setting, prices seem more readily
*In the case of quick cost pass-through and persistent wage-price spirals, wage-price controls must be completely
effective to be effective at all; any price rise generates pressure for price rises in other sectors. Unless
controls are completely effective, some prices will rise, generating still more pressure to raise prices or wages.
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raised than lowered. Therefore, as either demand or
costs fluctuate, price rises are not matched by price
'eclines. Of course, prices cannot rise very, far above
coats, because the high profit margin would eventually
encourage new firms to enter the market at lower prices.*
Current macroeconomic analysis seems to focus on
the use of aggregate fiscal and monetary policy instru-
ments. Yet these instruments may not be appropriate for
controlling inflation, if inflation is in large measure
due to sector-by-sector fluctuations in demand or cost.
If the current inflation, for example, is due to a ca-
pacity constraint in the energg'sector, aggregate policy
instruments can do little to solve the underlying prob-
lem. In fact, using monetary controls to combat infla-
tion has probably not only significantly diminished the
cost of energy, but has inflicted considerable damage on
the construction industry as well. The balance between
aggregate economic policies and policies for individual
sectors is important; single-sector testing can give
some indications on appropriate balance.
The final stage in single-sector testing allows the
previously exogenous inputs to respond to conditions
within the sector. Orders for the sector's output could
respond to price and delivery delay. Interest costs
could respond to the level of corporate borrowing and
the risk of loan defaults. As before, several new
feedback loops are formed which could modify the results
of earlier testing. The earlier results need to be
checked with the additional structure. The additional
structure also makes possible new behavior modes.
The Limits to Growth research (op. cit.) indicates
that industrial output and population may decline within
the next century, either unintentionally or intentional-
ly. This decline poses problems not frequently encoun-
tered in the present mode of long-term economic growth:
What happens when a sector's output and capital plant
must shrink? The diminution need not be gradual; in
fact, quite dramatic changes are possible. For example,
consider the financial standing of a sector for whose
output the demand is shrinking. In the past, if sector
operations were profitable, the sector could obtain the
financing it needed. However, as demand shrinks, fixed
costs reduce profit margins and weaken the sector's fi-
nancial position. Banks will usually still lend funds
to such a sector, however, in order to allow the company
or sector to acquire capital goods needed to operate ef-
fectively, and to repay both new and old loans. Past
some point, however, banks will not extend further credit
to a risky sector, or will extend credit at high cost.
The high cost or lack of adequate credit further weakens
the sector. Once this "financial watershed" is passed,
the financial condition of the sector deteriorates rap-
idly. Single-sector testing can indicate the situations
in which this deterioration occurs, and possibly how to
avoid it.
C. Double-Sector Testing
At present, the dynamics of even the production and
inventory portions of a two-sector model are not well-
understood. Yet to be explored are the various config-
urations of two sectors purchasing output from themselves
or each other, and phenomena such as entrainment. En-
trainment occurs when cycles in one sector give rise to
Comparable, in-phase cycles in another sector. Cycles in
the individual sectors of the economy must somehow be
entrained, if the aggregate national economy can experi-
ence uniform business cycles. So until the dynamics of
production and inventory cycles in the two-sector model
are better understood, assessment of the i'a,act of fi-
nancial considerations on cyclic behavior i.'quite
difficult.
As in the one-sector case, the analysis of the two-
sector model with respect to the financial equations be-
gins by making constapt the inventories and production
rates in each sector. The partial two-sector model can
then be used to investigate tentative conclusions of the
earlier tests. For example, the one-sector tests give
the circumstances in which a sector transmits almost all
cost increases to increased prices. Two-sector testing
expands upon the analysis by determining the circum-
stances (parameters and input values) in which two sec-
tors can generate a true cost-price spiral--prices of
the first sector increasing the costs of the second, and
vice versa. Another example of expanding upon the one-
sector results is the transmission of financial diffi-
culties. A two-sector model could. show the circumstances
in which financial difficulties in one sector cause fi-
nancial difficulties in the other sector via defaults or
delays on accounts payable, which further aggravate the
difficulties in the first sector.
A further stage of two-sector testing involves two
fully active sectors, including variable production, fac-
tor ordering, and product ordering. Then couple the two
sectors to one another by allowing interest rates and
loan availability to respond to the sum of the loan de-
mands from the two sectors. This coupling allows tests
of entrainment through interest rates and loan avail-
ability.
D. Conclusion
At this point, an important caveat must be stated.
The preceding text has emphasized the advantages of con-
structing and testing a model one piece at a time. This
step-by-step procedure is efficient only when the pur-
pose and overall structure of the model are already well-
defined. Without some idea of the problems to be ana-
lyzed and the policies to be tested, there is no basis
for either terminating the modeling process, or choosing
pieces to add to a model. Adding pieces to a model in
the vague hope of making the behavior more realistic is
a never-ending process.
Constructing, validating, and understanding models
one piece at a time is very practical for models whose
purpose and overall structure are well-defined. Construc-
tion is more easily performed with well-understood pieces.
Model behavior is more easily understood when the behav-
ior results from a simple model. A step-by-step approach
permits the national model and understanding of the be-
havior of the national model to grow gradually, without
the necessity of dealing with the full complexity of a
completed model.
In summary, each portion of the national socio-
economic model should be regarded likewise as a model,
with its own strengths and weaknesses. Each model exhib-
its its own characteristic behavior, and yields its own
implications for policy design. The step-by-step proce-
dures described above consist of nothing more than learn-
ing as much as possible from each of these models.
*The single aggregate production sector represents competition in markets by the values of the parameters governing
pricing and sector expansion. The production sector depicts entry of new firms into a market during periods of high
profitability by increases in orders for factors of production, and constraints-on further'price increases.
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