Using perceptions and data about the future to improve the simulation of complex systems

TECHNOLOGICAL

FORECASTING

AND SOCIAL

CHANGE

9,191-211

191

(1976)

Using Perceptions and Data about the Future to Improve the Simulation of Complex Systems THEODORE

J. GORDON and JOHN STOVER

ABSTRACT Many of the techniques used to forecast the future are basically extrapolative, that is, they assume that the future will be an extension of the past. This assumption will eventually be incorrect as new forces cause future changes. This paper describes methods for incorporating data and perceptions about unprecedented forces and events in otherwise extrapolative procedures. Two specific techniques incorporating these methods, trend impact analysis and probabilistic system dynamics, are described.

I. Introduction Extrapolation is a process by which information about a future state of affairs is gained totally from data collected in the past. The information content of historical data may be very high providing insight not only about continuous trends, but also about the expected variance about trends, correlations among variables, and cyclic components. Familiar examples of these forms of historical data analysis include: curve fitting to portfolio analysis involving describe trends using a fit “rule” such as “least-squares;” study of stock price variance as a measure of volatility and risk; regression analysis in which two or more variables are described in terms of their joint patterns of historical evolution; and Fourier analysis in which the spectrum of frequencies contained in an historical sample is determined. This historical data can yield many different forms of information about the past: trends, variance about a central trend, correlations among variables, and frequency content and periodicity. In extrapolation, it is assumed that one or more of these components of historical data will remain constant and, in this respect at least, the future will be like the past. Inevitably, this assumption will be incorrect. Forces in the future will be different than in the past and these forces will change trends, variances, correlations, and higher frequency components. Some systems can change more rapidly than others; in this respect, some systems may be thought of as having high or low inertia; nevertheless, all systems can change as a result of unprecedented forces and such forces diminish the accuracy and usefullness of extrapolation. The situation is similar to a bullet being tired from a gun. The course of the bullet may be calculated quite accurately ceteris paribus, given only the information present at the time it leaves the muzzle. This information, as all historically derived information, is Theodore J. Gordon is President of The Futures Group, Stover is a member of the senior staff of The Futures Group. 0 American

Inc.,

Glastonbury,

Elsevier Publishing

Connecticut.

Company,

Inc.,

John

1976

192

THEODORE

J. GORDON

and JOHN STOVER

descriptive only of past trends, variance about those trends, correlations among descriptive variables, and the frequency content of the variables. All of these pieces of information are useful in forecasting the bullet’s position in the barrel but are insufficient in determining position beyond the muzzle. Here, unprecedented forces are possible; for example, wind shear, gravitational acceleration and gyroscopic precession, and interception with a target are not anticipated in the historical data. Such forces constitute information about the future. The degree to which the bullet responds to such forces depends on several factors including the strength of the forces and (literally) the bullet’s inertia. Note that the unprecedented forces mentioned are intrinsically of different types. Wind shear is probabilistic, that is, its presence in the future is expected because such phenomena have been observed in the past and there is a chance they will appear and be important in our case as well. Gravitational and gyroscopic acceleration are certain and represent newly imposed biasing conditions. The target represents a class of low probability, high impact, events-one of a number of possible “surprises”. In a more general sense, information about the future which is not reflected in historical data include’s: _ Boundary conditions which fix limits to extrapolations; - Biasing conditions which shift the patterns of development of historical data; - Unprecedented events which when they occur are reflected in “deflection” of the extrapolations. Such events, if low probability and high impact, are surprises. and “patterns of development Note that in the above descriptions, “extrapolation” historical data” should be interpreted as including all of the information elements historical data-trend, variance, correlation, and frequency content.

of of

We maintain that: - Extrapolation can provide an accurate forecast if and only if unprecedented forces and events such as those mentioned above are highly improbable or are of extremely low impact. - Combining information derived from historical data with perceptions and data about unprecedented forces and events is necessary in forecasting. - Systematic methods for generating sets of unprecedented events and forces, for estimating their probabilities and impacts, and for including them in extrapolative processes, are possible and constitute a most important direction in future research. Extrapolation is, of course, a technique not confined to the simple process of extending a curve which tits a time series of data. For example, econometric processes typically use statistical techniques to search for significant correlations between the variable to be predicted (the dependent variable) and various orthogonal predictor variables (the independent variables). Once these correlations have been established, the relationships among the variables which worked so well in the past are often assumed to remain constant in the future. If historical increases in gasoline consumption can be expressed in functional form as being dependent on changes in disposable income, and the number of people above the age of 21 and below 68, then it is extrapolative to assume that this relationship will hold in the future. It doesn’t matter whether the relationship is complex and involves 15 variables-whether the relationship includes the static input/output matricies or other sensitive analysis techniques-the assumption is still the same: historical relationships will hold in the future. Such relationships are often useful for short term forecasting but shed little insight

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193

into causality. System dynamics, on the other hand, focuses on causality and produces systemic models which “explain” historical developments by defining the linkages among state variables and rate determining features of closed or semi-closed systems. Subtle and powerfully descriptive simulations have been constructed using such techniques. In many instances these have been validated as forecasting tools by comparing their output over historical time intervals, not only in terms of absolute levels but intrinsic periodicity and response to excitation. Yet, system dynamics models are also basically extrapolative. They assume that the system which explains past development will continue to do so in the future. With system dynamics, however, many relationships are based on judgment and are not determined by historical data. The modeler can, therefore, include in the model some of his perceptions about the future. For example, when the relationship between two variables is assumed to be non-linear, the exact relationship is determined by history for ranges of the variables covered in the past but is determined by the modeler for values of the variables that have not occurred historically. At The Futures Group we have begun to develop techniques for explicitly incorporating data and perceptions about unprecedented forces and events in otherwise extrapolative methods, including econometric and system dynamics techniques. We believe this is an important frontier of methodological research which will not only improve forecasting accuracy and the understanding of uncertainty in forecasts (and indeed in the future itself) but will also help establish the sensitivity of future conditions to an array of forces for change and thus will contribute to the analysis of policy. In this paper, some methods for incorporating unprecedented forces in otherwise extrapolative situations are described, beginning with a simple example of some of the principal considerations, and then describing recent approaches taken in analyses over the past three years at The Futures Group. II. An Illustration of Concepts Suppose that we wished to produce a forecast of the maximum speed of aircraft sometime in the future. Suppose further, that we had good historical data about the aircraft and airline industries, demand for travel, costs, price elasticity for travel of various sorts, and so on. To obtain the forecast, using different extrapolative techniques, we could perform one of the following operations: - Using only historical data about aircraft speed versus time, we could fit a curve to the data points, limiting its order by judgment (in itself an assumption about the future) and produce an equation of the form

where V, is the maximum speed of a commercial aircraft at any time t and A and B are constants. Such an equation might be derived by using a least squares fit procedure. (The choice of the form of the extrapolating equation is not trivial. A straight line was used in the example but many other forms are useful. For example, Fisher and Pry in their work on substitution theory use a S-shaped curve to forecast the future substitution of one technology for another or to forecast the market share gained by one product at the expense of another. [I] They justify the use of this curve shape on the basis that it has been demonstrated in many past substitu-

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THEODORE J. GORDON and JOHN STOVER

tions. In the spirit of this paper, we would ask whether future developments could change the shape of the curve.) - Using historical data about aircraft speed and other historical data about, say, the economic climate and the cost of travel, the form of the equation might be V, = A + B(GNP) + C(TC)

where, GNP is the Gross National Product and TC is a measure of total cost. Such an equation might be derived by the process of step-wise regression. - Using all the data at hand, a system dynamics model might be constructed to explain the dynamics of new aircraft generation in response to travel demand and economic forces; the outline of such a model might be as shown in Fig. 1. Here econic factors affect the viability of the airline and aircraft industry as well as affecting demand. Anticipated demand leads the airline industry to order aircraft. After a delay they are delivered to satisfy demand within the aviation system. Real demand by that time may or may not be equal to anticipated demand, thus giving rise to dynamic behavior. In all cases, the forecasts depend on historical data and thus are extrapolative. the future forces and events which could change the situation:

Imagine

- Reaching a maximum speed beyond which increasing speed is incredible (for example, 18,000 m.p.h., at which point orbital speed is reached). - Changing lifestyles which greatly reduce the demand for travel, changing past notions about elasticity. - Adoption of legislation making aircraft with certain characteristics illegal. - A breakthrough in technology greatly reducing the costs associated with achieving certain speeds or aircraft types. (These examples, of course, represent, in turn; a boundary condition, a changing bias, an unprecedented event, and a surprise.) How could such events be included in the three forecasting approaches mentioned earlier? For all three methods, time series extrapolation, econometric regression, and system dynamics, the new boundary condition can be imposed directly. For example, in time series extrapolation the boundary condition can be simply expressed as another condition which must be met by the curve which fits the given data points. For new biasing developments or unprecedented events, the problem is somewhat more difficult. The time series equation could be written:

v t =(AtP

x q+(BtP ax

x qt. ax

Where x represents a biasing development or unprecedented event and its probability at time t is P,. The partial derivatives indicate how the constants would change in the presence of the development x; this change is “derated” by P, to account for the fact that the event is not certain. Sometimes there is physical significance to such partial derivities and, in these instances, judgments about their magnitude may be sought directly. For example, an expert can be asked “How is the rate of change of speed likely to be influenced by the occurrence of the biasing development x?” The answer to this question is, of course, aB/ax..

PERCEPTIONS ABOUT THE FUTURE AND SYSTEM SIMULATION

195

Fig. 1. A system dynamics model outline. In

the case of the econometric

approach, the form of equation

becomes:

Now the problem is complicated by the fact that, in general, there is no physical significance to the constants A, B, and C, hence there is no simple way to inquire and collect judgments about these partial derivitives. If these partials are assumed to be zero over a short forecasting interval, that is, if the system is assumed to have a reasonably high inertia (and therefore that A, B, and C, remain constant), some improvement in accuracy is probably achieved by including the other partials, aGNF’/& and aTC/ax. When a series of independent events are involved, the equation form becomes: i3A Vr=(A+Pxax+Prg If the events are not independent,

aA

. . .)+(B+P,

aB dB ax +Py ar . . .) . . .

they will exhibit cross impact effects

which should also be included if significant. As for system dynamics, the approach is generally the same; that is, the coefficients and variables of the equations linking the state variable can be modified, probabilistically, for the anticipated effect of the unprecedented event or biasing development. The ability to estimate or judge such impacts is higher than in the case of econometric forecasting, since in general the coefficients have physical significance. In some cases, the effect of unprecedented events will be to change the structure of the model. For example, the adoption of restrictive legislation might add a new sector on regulation to the model, as shown in Fig. 2. There are obvious problems with these approaches including most prominently the inability to form a complete list of impacting events and the difficulties and inaccuracies involved in estimating or computing probabilities and impacts. Furthermore, the approach described above assumes that the partials remain constant over wide changes in

196

THEODORE

1 I I I

1----t

J. GORDON

and JOHN STOVER

PERCEPTIONS

ABOUT THE FUTURE

AND SYSTEM

SIMULATION

197

the variables (although this assumption is not required in some techniques described later). Nevertheless, practical approaches which show promise are being derived and utilized in pragmatic situations. The next sections of this paper describe several such techniques. III. Trend Impact Analysis Trend Impact Analysis (TIA), an analytic procedure newly developed by The Futures Group, divides the task of extrapolation in such a way that human beings and computers are assigned the tasks that each does best. First, the computer extrapolates the past history of a trend. Second, the human beings specify a set of unprecedented future events and developments and how the extraplation would be changed by the occurrence of each of these. The computer then uses these judgments to modify the trend extrapolation. Finally, the person evaluates the resultant adjusted extrapolation and modifies the input data to the computer in those cases where the output appears unreasonable. Figure 3 schematically shows this procedure. MATHEMATICAL

TREND

EXTRAPOLATION

The development of a surprise-free extrapolation is the first step in the TIA process. A computer program selects the “best-fitting” curve from a set of alternative equations. This curve is then used to provide the surprise-free future extrapolation. At the option of the program user, in order to avoid unreasonable extrapolations, the program can either truncate extrapolations that fall outside upper or lower bounds, or select the “best-fitting” curve only from among those that do not give rise to extrapolations falling outside the specified bounds. Alternatively, the user can reject the mathematical extrapolation generated by the TIA program and supply an extrapolation developed by some other curve fitting program or one based entirely on human judgment. Several refinements in the programming of this aspect of TIA enhance the effectiveness of the best-tit test and extrapolation procedure.

(1) It

is not necessary that the data cover a continuous span of time. Data in which there are gaps are fully acceptable-the program makes use of whatever data are available, taking into account any gaps, but without being stymied by them. (2) The program does not give equal weight to all data. Rather, a year may be specified (normally the present year) for which data are to be given maximum weight. As the times to which the data refer are further removed from the year which has maximum weight, the data are given less weight.r This procedure thus takes into account the possibly lower reliability of data that are more distant in the past or, more important perhaps, the lower influence on the future of developments that have occurred progressively farther in the past. The formula chosen also makes the sum of an infinite number of weights infinite, rather than convergent, so that even very distant years continue to have a finite contribution. (3) Since there is no guarantee that a mathematical extrapolation will give a good lit to the given data, the TIA program reports to the human user just how good the fit was, using the same squared correlation coefficient that determines which mathematical formula should be used. Where judgment or analysis indicates a

’ The weighting weight.

formula

is

1 (112 + y--Y&

where y is a given year and y0 is the year given maximum

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THEODORE J. GORDON and JOHN STOVER

. . .

2 E .gj f

PERCEPTIONS ABOUT THE FUTURE AND SYSTEM SIMULATION

199

more realistic set of data should be used, it can be input directly as part of the specified data used for subsequent steps. HUMAN JUDGMENTS OF EVENT IMPACTS

Human judgment and imagination are central to the second step of TIA. Here, the program modifies the surprise-free extrapolation to take into account important unprecedented future events. First, a list of such events is prepared. These events should be unprecedented, plausible, potentially powerful in impact, and verifiable in retrospect. The source of this list of events might be, typically, a literature search, a delphi study, or a consensus among consultants. Whatever the source, the events selected comprise an inventory of potential forces which would lead to a departure from a suprise-free future. Several judgments are made about each selected event. First, estimates are made of the probability of occurrence of each event as a function of time. Second, the impact of each event on the trend under study is estimated. Impacts can be specified in several ways; our procedure (Fig. 4) involves specification of: (1) The time from the occurrence of the impacting event until the trend begins to respond. (2) The time from the occurrence of the impacting event until the impact on the trend is largest. (3) The magnitude of that largest impact. (4) The time from the occurrence of the impacting event until the impact reaches a final or steady-state level. (5) The magnitude of that steady-state impact.

DEGREE OF IMPACT

EVENT OCCURRENCE

(E.G., %, ABSOLUTE AMOUNT)

TIME 70 lS:+ N)TICEABLE IMPACT

I TIME

TO

MAXI~UI

1MPAW---+ I I

i c-1

Fig. 4. Event impact estimates.

TIME

x)

STEADY

STATE

OR CONSTANT

Ib’?ACT-~

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THEODORE I. GORDON and JOHN STOVER

The two impact judgments are taken to be completely independent. For example, the maximum impact might be positive, and the steady-state impact negative, or the steadystate impact might be zero, meaning that the impact is only temporary. Finally, the maximum impact might be the same as the steady-state impact. In addition, impacts can be specified in either relative or absolute units-i.e., they can be specified as a percentage change in the values of the trend at the time of impact, or they can be specified in absolute units of magnitude of the trend. For example, the impact of a particular event on the number of dentists could be specified either as a 10% decline of that number or as a downward shift of 12,000. The form used to record these estimates is shown in Fig. 5. COMPUTER PROCESSING OF IMPACT ON EXTRAPOLATED

TRENDS

The heart of TIA is the computer program for using these judgments to calculate the expected impact of the selected events on the extrapolated trend. A closed-form procedure is used to solve this problem. The expected value, or mean, of the impact and upper and lower quartiles of the distribution of possible impacts are computed for each indicator. The expected value of the impact is computed by summing the products of the probabilities of the impacting events for each possible year and the magnitude of their impact, taking into account their specified lags. Probabilities of events for years not specified are estimated by linear interpolation, assuming that an event has 0.00 probability at the present time. Similarly, impacts are linearly interpolated between the three specified impact magnitudes. As described, this approach treats the coupling among the impacts of the various events as negligible; however, if such interactions are believed important, they can be included using cross impact techniques. Thus, the impact estimate is produced as the sum of independent random variables. The net result is that the variance of the impactadjusted forecast is the sum of the variance of the trend extrapolation (as measured by the square of the standard error of estimate) and the variances of the impacts of the associated events. Thus, where Pye is the likelihood that event e will occur in year y, and u,,~__~,e is the impact that event e would give rise to (v~-Y) years after its occurrence, the expected value of the impact in year JJ~ would be

cc’

e

Y=Y,

PY@Y k-Y

,e

where y, is the present year (e.g., 1974). (See Fig. 6.) TYPICAL TIA RESULTS

Use of the TIA procedure has revealed that important insights may be obtained by utilizing this form of trend extrapolation. The development of improved trend forecasts is only one of the advantages of this method. Insight into how adjustments of event probabilities and impacts vary the estimated future value of the indicator in question, in terms of both the median and interquartile range, can also prove to be very useful in developing an understanding of the effectiveness of policies or actions which may be available to us. Forecasts of the indicators shown in Fig. 7, Percentage of Pharmaceutical Manufactur-

SIVXE

WIT

CRLG PA’XUIKI

Fig. 5. Format for event impacts.

Cflii7

ACCC3.X

FOR

I .99

1975

ESTIPATEC PROBABILITY

YcvtRs TO FIRST I VJ’ACT

ESTiNATES PROVIDED

.-‘-_

M4XIlQ4 IWAtT CPERCENT)

BY MPERTS

YVRSTO STWY STAT! IYPACT

2;

s

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THEODORE

1’S

-

-197s

1 ‘75’

*O

1976

1 ‘76’

1977

*I

J. GORDON

1 ‘7Cx

lY78

*2

and JOHN STOVER

1 ‘76’

‘3

19?9

Fig. 6. Expected value of an event impact.

ers Sales to Hospitals, Clinics, and Laboratories and Average Cost of a Prescription are drawn from a recent report which is part of the new data service (called PROSPECTS) recently developed at The Futures Group. The forecasts in the PROSPECTS reports are prepared using the TIA procedure and, as they represent material prepared to aid in real-world decisionmaking and planning, should prove useful in discussing the insights obtained from using TIA. The forecast of Sales to Hospitals, Clinics, and Laboratories follows a familiar pattern found in many trend extrapolations-the projection has no inflections and depicts the future as essentially an extension of the past. In the case of Average Cost of a Prescription, we see that the forecast is markedly different from a conventional trend extrapolation of historic data, and it has some interesting inflections. Tables 1 and 2 list the events used in constructing each forecast along with their probabilities of occurrence and the nature of their impact. IV. Probabilistic SYSTEM

System Dynamics

DYNAMICS

System dynamics was developed in the 1950’s by Professor Jay Forrester of the Massachusetts Institute of Technology. The original concepts were derived from servo-

Drug News Weekly, The Drugstore-U.S.A., varibus issues

Fig. 7. Typical forecasts obtained by using trend impact analysis (TIA).

SOURCE:

P!ZCEWTAGZ OF PHARXACEUTICAL MANUFACTURERS' SALES TO HOSPITALS, CLINICS, MD LABORATORIES

SOURCE:

Pharmaceutical Manufacturers Association, Prescription Drug Industry Fact Book -- 1973 (Washington, D.C.: Pharmaceutical Manufacturers Association, 1973),p.27

AVERAGE COST OF A PRESCRIPTION

Analysis

Forecast

of Percentage

of Pharmaceutical

Manufacturers’

1

Widespread availability of certain minimal care facilities attached to hospitals for persons not needing acute care (pre-admission workshops, convalescence, regulation of diabetics, stabilization of cardiacs). Most major insurance companies limit to one day pre-surgery payments, encouraging more out-patient testing. Nearly all hospitals actively participate in FDA’s adverse drug reaction reporting system. 25% reduction in highway accident rate. AU hospitals required to have utilization committees which review length of stay and determine when a nor´ patient should be transferred to extended care facilities. Computerized medical histories among health care facilities in a Standard Metropolitan Statistical Area. Forty percent of the population receives annual multiphasic screening. Comprehensive compromise health care package initiated. In-patient costs increase twice as rapidly as consumer price index. Consolidation of proprietary hospitals resuls in the virtual disappearance of most hospitals with less than 200 beds. Change in population distribution: aged 65 and over increase by 25%; those 55 to 64 increase 17% over 1973 levels.

Events Used in Impact

TABLE

0 0 0 2 1 0 0 0

1980 1980 1980 1980 1982 1980 1980 1980 1985

.40 .lO .30 .50 .65 .90 .50 .60 .99

10

0

1980

.50

0

1984

Years to fiist impact

5

10 5 5 5

15

0 0

10

+10

-3 -2 -1 +5

-5

-5 -5

-0

-10

-15

20

0

Maximum impact (percent)

Years to maximum impact

Clinics, and Laboratories

.60

Estimated probability by year shown

Sales to Hospitals,

2

Abolition of all drug product brand names; standard abbreviations devised for generic names. Drug reimbursement in all federally-funded health programs based on a Maximum Allowable Cost (usually generic drug price). Removal of all federal and state restrictions on prescription price advertising. Decrease in the average size of prescription by 20%. Comprehensive health care package initiated, federally run, federally subsidized. Period of patent protection reduced to 5 years after market introduction of a product. Economic recession (similar to late 1950’s). (Recession: Sustained drop in real GNP greater than 2% for at least 6 months.) Federal and state legislation to allow paraprofessionals to perform more drug-dispensing duties. Anti-substitution laws repealed in most states. Semi-automated drug-dispensing equipment for use by pharmacists. Number of prescriptions per user increases 10% over 1973 levels.

Forecast 1985 1976 1980 1985 1980 1984 1980 1984 1985 1980 1980

.lO .75 .20 .lO .50 .40 .35 .25 .44 .50 .40

by year shown

Estimated probability

Events Used in Impact Analysis of Average Cost of a Prescription

TABLE

5 10 10 10

1 2 1

2 2 10 1.5 2

5

5

Years to maximum impact

5

0 0 2 5 10

5

5

Years to first impact

-5 -2 +5

-5

-10 -10 -10 -15 -10

-15

-20

Maximum impact (percent)

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THEODORE J. GORDON and JOHN STOVER

mechanism analysis in which systems are depicted as a series of interlocking feedback loops. Often many simple loops interact with each other, producing complex systems. For example, Fig. 8 depicts part of a model of the Japanese economy recently developed by The Futures Group. In one feedback loop, increasing industrial production increases demand for energy. This increased demand will normally lead to increased supplies and increased stocks of energy supplies. These increased supplies will, in turn, allow increased energy usage and increased industrial production. The supply of energy comes from domestic Japanese resources and from imports of foreign resources. A second crucial point in the modeling of the decisionmaking process is the effect of delays. Often the decisionmaker does not have up-to-date information about his environment. He is, therefore, making decisions on the basis of what the situation used to be, rather than what it now is, or is taking action that will not translate into concrete changes until some future time. System dynamics models normally describe the causal connections among system variables. These causal linkages, coupled with the fact that such models attempt to provide a complete description of the system, make system dynamics models quite useful in studying system behavior and in analyzing policies. These models can also be used to study the effects of unprecedented events one at a time. However, considering events singly is not always adequate. The occurrence of one event usually affects the likelihoods of other events. These complex interactions have been recognized and studied during the past few years through the use of cross impact analysis [2,3]. PROBABILISTIC

SYSTEM DYNAMICS

Probabilistic system dynamics uses the concepts of cross-impact analysis to add the expected impacts of future events to system models. As an example of the influence of events on model structure, consider the simple energy system discussed earlier and presented again in Fig. 9. In this figure, however, new loops have been added (dotted lines) that correspond to the impacts of events. The energy supply fraction represents that fraction of demand that is filled by available supplies. Although abundant energy supplies kept this fraction equal to or greater than one in the past, future energy shortages may well cause it to fall below one. When this fraction falls below one (indicating.energy shortages) the probabilities of various events are affected. For example, the probabilities are increased for two important energy events (that Japan and the USSR engage in the large scale development of Siberia and that because of a surprising technical breakthrough, fusion power is developed rapidly and is implemented in Japan). The second event upon occurrence increases the supply of atomic power, thus increasing domestic energy supplies. The first event, upon occurrence, will add significant new supplies of natural gas to Japan’s energy picture (natural gas supplies today are an insignificant energy source for Japan). Thus, not only is a new fuel added to energy supply (as well as all the important price and fuel trade-offs that are a part of that new fuel), but imports, balance of payments, and exports may be affected as well, depending on the exact nature of the trade agreements. These events may also affect other events in the cross-impact matrix that will, in turn, influence the model in other ways. The impacts of events on the basic model can be calculated in one of two ways. One method is to calculate the expected value of the impact, that is, calculate the value of the impact if the event occurs and then discount this impact by the probability of occurrence. In this manner all of the events have some contribution to the basic model. Of

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THEODORE

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course, if only a few events are considered this type of probabilistic calculation has little real meaning. Fusion power will either become an energy alternative or it will not. To say that atomic power will supply 25% of a country’s needs because fusion power has a 50% probability of being developed would be absurd. Rather we should say that atomic power will provide 35% of energy needs if fusion power is developed and 15% if it is not. However, if our real concern is not the percentage of energy supplied by atomic sources but the total availability of energy, then expected value impact considerations begin to make sense if a few more events are included in the model. Suppose events concerning the development of needed technology for oil shale, tar sands, solar electricity, geothermal drilling, etc. were included. We may not be able to say with certainty that any of these developments will or will not take place, but we can say that some of them will probably happen while others will not. By combining the probabilities of occurrence of these events with their expected impacts, we can develop a model that will indicate the expected future supply of energy. It will not determine which events actually occur or what the real fuel-mix will be (as this will depend on actual event occurrences), but it can give a better indication of the total energy supply than if these events had been entirely omitted. Furthermore, the effects of policy decisions which can influence the development of different energy technologies included in the model can be displayed in terms of the expected influence on the total supply of energy. It is in handling these kinds of policy considerations that the main contribution of PSD lies. The other method by which impacts may be calculated involves actual occurrence or non-occurrence of the events. Any event might be considered to occur at that time when its cumulative probability exceeds some previously defined value, SO for example. Thus, in a run of the model, events would impact the model only after each event “occurs” (the cumulative probability exceeds the occurrence value, SO). Upon the occurrence of an event the model is changed to reflect the full impact of that event at that time. Some events may, of course, never occur within the time span of the forecast. Policy changes that affect the basic model or event probabilities will affect the probability distributions of some of the events (through direct policy impact, model impacts, or other event impacts). The occurrence pattern of events in the future will, therefore, also change. The choice of method to be used for calculating event impacts depends on the particular situation and the ultimate use of the model. If expected value impacts are calculated the event set should normally be on a much more specific level of detail than the main output variables of the model. Thus, if the variable of major concern in a model is total industrial output, events might describe the introduction of new energy sources (fusion, geothermal, etc.). However, if the major output variable is the total supply of atomic energy, events should describe advances that might be a part of the fusion development process (progress in laser technology, magnetic containment, etc.). Expected value impact calculations may be preferred in cases where large numbers of events are involved and the main purpose of the model is to display expected future values of major system variables. When the major use of the model is to study system behavior, rather than to produce expected value forecasts of specific variables, the occurrence/non-occurrence method of impact calculation would typically be most useful, as it corresponds more closely to real world behavior. It should be recognized, however, that the occurrence/non-occurrence cut-off level (SO to .70 or whatever may be chosen) is entirely arbitrary. The sensitivity of the results to this figure should be thoroughly explored. In order to develop a PSD model of a system, two processes are followed simulta-

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J. GORDON

and JOHN STOVER

neously: the development of a basic system dynamics model and the identification of the elements of the cross-impact matrix. The identification of the event set and the estimation of probabilities and impacts can also serve as an excellent first step in the integration of decisionmakers into the modeling effort. The Delphi approach to information gathering may, in many cases, be applicable. The first step in the development of the cross-impact matrix involves estimating the time dependent probabilities of each of the selected events; the impacts of events on events are then described. For example, if one event is that a new method of reclaiming and recycling scrap zinc at one-third the cost of new zinc production is developed this event might originally have a probability of occurring by 1985 of .15. However, if another event, that proven world reserves of zinc quadruple through new discoveries, were assumed to occur, it would have substantial impact on the probability of the first event, possibly reducing its probability by 1985 from .I5 to .05. The impacts of the events on the model are then described. These impacts may come from expert judgment in cases where the impact is uncertain or they may be calculated when possible. These impacts may take several forms. The actual structure of the model may change, coefficients of the equations may vary, new terms may be added to or subtracted from equations, etc. Some variables in the model will also have impact on the event probabilities. These impacts are also estimated and included in the cross-impact matrix. As an example, assume that the supply of zinc to some country is a factor in an economic model of that country. The supply of zinc would undoubtedly depend on domestic demand for zinc, world demand for zinc (competing with domestic demand), domestic supplies of zinc ore, world suplies of zinc ore, and the price of zinc. However, if the event discussed earlier concerning the development of a low cost zinc recycling technique were to occur, the above relationships concerning zinc supply would have to be altered. Zinc could now also be supplied through scrap recycling (an addition to the supply equation), and domestic and world stocks of products containing zinc and their obsolescence rates now become important as well. This illustrates one type of impact of an event on a model. In turn, model variables, the shortage of zinc, for example, would affect the probability of the events (by causing increasing exploration for new resources and increasing expenditures for new recycling techniques). A run of an entire model constructed using probabilistic system dynamics involves the simultaneous operation of a DYNAMO computer program (the basic model) and a FORTRAN IV program (the cross-impact sector). The computational sequence consists of the following steps: (1) Initial values for the model variables are used to compute new values for those variables for the first solution interval (a year or part of a year). (2) These new values are transferred to the cross-impact matrix. (3) New values of event probabilities are determined from the original values and the impacts of the model variables. (4) The impacts of events on events are calculated using the probabilities of the events and the occurrence and non-occurrence impacts. (5) The probabilities from the cross-impact sector are transferred back to the basic model, event impacts on the model are calculated, and the basic model is revised accordingly.

PERCEPTIONS

ABOUT

THE FUTURE

AND SYSTEM

SIMULATION

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(6) New values for the model variables are calculated for the next solution interval using the model as revised by the impacts from Step 5. (7) Steps 2 through 6 are repeated until the end of the time span under study. Sensitivity analyses can be run to test the sensitivity of the model to the event probabilities, impact estimates and model assumptions. Policy tests can be run by deciding how specific policies would change the model (event probabilities, model structure, impacts), making the appropriate changes and rerunning the model. The main advantages of probabilistic system dynamics are: (1) The inclusion of events in the model allows occurrences outside the area of focus of the basic model to be taken into account in the model predictions. In this manner, any number of exogenous events may be included, thus, the scope of the model is not limited strictly to the closed system defined by the system boundaries. (2) The structure of the basic model itself becomes dynamic. Relationships among variables and even among sectors of the model may change with time as the impacts from other parts of the model and from the events accumulate. (3) Policies can be tested in terms of their effects on the relationships among model variables, model structure or event probabilities. Policies that have their main impact on areas outside the basic model can still be tested for impact through the effect of those policies on exogenous events. V. Conclusions

TIA and PSD are two examples of procedures by which perceptions and data about future events can be included in basically extrapolative forecasting approaches. Both are crude but even in their present form, quite useful. At The Futures Group, perhaps 200 times series indicators have been forecasted using TIA, and at least three PSD models have been or are being built (Japanese economy, the American livestock industry, and economic growth and income distribution in developing countries-specifically in Uruguay). Has accuracy been improved? It is difficult to say categorically, although a number of cases exist in which TIA has produced realistic changes in slope and trend reversals which would have been missed by conventional extrapolation. Certainly the analysts using the tools gained insight about the significance of future events which would not have been possible without the use of probabilistic approaches. References 1. 2. 3.

Fischer, John C., and Robert H. Pry, A Simple Substitution Model of Technological Change, Technol. Forecast. Sot. Change 3, (1) (1971). Gordon, Theodore J., and H. Hayward, Initial Experiments with the Cross-Impact Matrix Methods of Forecasting, Futures 2, (2) (1968). Gordon, Theodore J., Richard Rochberg, and Selwyn Enzer, Research on Cross-Impact Techniques with Applications to Selected Problems in Economics, Political Science, and Technology Assessment, Report R-12 (Middletown, Conn.: Institute for the Future, August, 1970).

Received October 13, I975