Some notational tools for forecasting and model building in the social sciences

by Gunnar Sommestad, 1981


The two kinds of abstraction or modeling

A study of the future or any problem concerning strategy, choice or risk can have a tendency to follow one of the two lines of thought that I will now present.

One way concerns the fact that it is possible to arrange a discussion or a report in such a way that you can closely follow a number of chosen developments or processes. These developments or tendencies can be discussed thoroughly, relying on the specific properties that seem to be inherent in the processes themselves. This way of reasoning is very often found to be the natural way and the further path of the development can often be forecasted accurately. In this way of reasoning stress is laid on continuity, context and survival of a phenomenon, an organization etc.

The alternative method and what I will describe as the opposite way of viewing the social and economic reality can often be found in system analysis studies and is the most common viewpoint of the economists. This alternative way of looking at things emphasizes different mutual dependencies within a bigger system. Choices, tradeoffs and uncertainties can thus be demonstrated in a better way.

My belief is that this distinction has its root in basic properties of the human perception system. I think an effort should be made to study these properties, and work out and define the theory and scientific concepts that correspond to that psychological reality.

The basis of this aim are of course some philosophical premises saying that functional properties of human perception should have a guiding influence on the choice of social science working methods. It is not possible to justify that point of view here, since it requires a purely philosophical treatment.

The problem

Economic concepts and economic methods have long been blamed for inability to supply decision data and proper guidance in many political and social areas, the debate about ecological system function vs. economic criteria perhaps being the best example. There have been many attempts to solve these problems.

Some proposals have been made within the economic science, as for instance cost benefit analysis and non-economists have made many proposals. The proposals of the non-economists ('ecologists', business economists, etc) have often been accompanied by furious attacks against some of the central methods and concepts in traditional economics. They have usually been less successful than cost benefit analysis, but I do not think that this observation settles the matter.

My basic view is that the concepts of economics are the tools best suited to be developed to fill the gap between economics and the other 'criticizing' disciplines, but it should not be made by using very refined ideas like 'consumer surplus' or 'material balances'. Instead the work should start at a more basic level with the notion that there is in most situations in life and nature a trade-off, or some kind of exchange rate. This holds for markets, it also seems to hold to some extent for ecological and sociological environments.

Basic models

The aim is to create a balance between on one hand the idea of processes and on the other hand the idea that there are terms of trade in most things and situations.

I propose that we call the terms of trade or economic way of reasoning the first dimension.

The plane abstraction of the first dimension

The first dimension is a stationary system, a frozen picture of reality and it is meant to display cross-sectional relationships. It is of course not true at all that economics is only that, but I think that the caricature contains some truth. I hope that you can accept it for the purpose of displaying contrasts.

Let us generalize the terms of trade or price relationships to a new very general concept called relation. A relation will of course be a function of physical material states, changes and processes and the human perception and structuring of reality. (As I said, before, I leave the philosophical side of the matter. However, a good concept or semantic construct should be able to take care of itself without philosophical proofs.)

Let us turn to what I call the second dimension. The second dimension describes reality as a set of processes. The objects are viewed in a time perspective. Of course the observed processes or developments are also some kind 6f projection of the underlying reality, or whatever philosophy you prefer.

The process connections of the second dimension

The scope of analysis

The concept of a boundary line between the set of known objects or commodities, 'A' and the rest of reality is introduced. It is because I want to illuminate the fact that we make a demarcation of the area studied, perceived. I think that anybody who knows of cost benefit analysis understands my point here. The idea is to make the boundary line between economics and the non-economic world something more than a nuisance to the cost benefit analyst.

The demarcation should be understood instead as a natural moving border, a border that permits changes of the economic environment.

The symbols

I have made some alphabetical symbols, and we let X symbolize the objects or commodities of the first dimension. r symbolizes the relation. Thus XrX could symbolize the typical link in a first dimension theory.

1st dimension properties

The point is that man has a tendency towards abstract thinking and model building into a network, rather like the visual plane in which the model or theory could be laid out.

The X and the r represent distinct but rather empty structural concepts. A link exists or it does not exist; We need some software residual factors. The residual factor of the first dimension link will be called p. This is of course the price and also what could be called the generalized price, the idea of the terms of trade function.

The set of objects and links known to the analyst or the citizen, that I called "A", is stable and well known here. It is natural to be rather sure what we talk about in a theory that can be abstracted in this way and laid out as a network. I say this because most things will be the very opposite when we get to the second dimension, the processes.

2nd dimension properties

A process or development is a logically connected and continuous process between two points of time. These points are some kind of nodes or inflexion points. Maybe you recognize the decision tree and the critical path method of project planning in this.

Where shall we put those inflexion points? Well, it depends on the situation. There are beginnings and ends of processes. This distinction has not got the clarity of the commodity concept, but as an abstraction it is neither better nor worse, I think.

In the alphabetical notation I call the process yIy, I for integration. When we look into the future, the future looks uncertain and not stable. We seek stability and want to know the probability of future events or alternatives. Therefore we invent the abstraction that there is such a thing as a development, starting in time now or time y1 and. continuing undisturbed to time y2. Of course we do not know everything about the future, therefore we invent the probability concept. The probability can be seen as an interpretation of the residual factor P in the chart here.

However, probability is a more hardware concept or positivistic type concept than the terms of trade (or price) concept 'p'. Therefore capital P for probability.

I do not think that we do try to abstract the second dimension into a two-dimensional plane or a net structure. It is better represented by the set of vectors put alongside each other.

The demarcation A is unclear in the second dimension. The forecaster tries to extend it and says to the decision-maker that the future is an area of choice or dealing. This is a symbolic picture.

The static, mutually restricting system

Dualistic character of economic objects and actors

If you prefer you can assume that the X and y concepts are a projection that comes from some kind of real underlying element which I call z (residing in the locus 'w').

One basic idea is that the z elements are projected both into the first and the second dimension, but the projections from the obscure z may well be understood as rather different when they are commodities X and when they are processes yIy.

An example here; Assume that we are talking about a car industry. The point is that the car industry as a part of a network with static theory relationships must not necessarily be the same concept as the car industry being described as a company, an organism surviving and evolving in time. You might find this ridiculous but I think that there are small distinctions like these that could be keys to some bigger problems.

I have now tried to describe (or propose) two opposite ways to abstract economic matters. It seems to me that it is not possible to reconcile these two ways harmonically into one system. They simply do not meet. However, intuitively we do combine them, so there must be some kind of interaction. In my paper I have made some speculative remarks about this. We sometimes infer from the timeless static theory to developments - (most recommendations made by economists are like that...) - and sometimes we move the other way. For instance time series studies often lead to conclusions about relationships in a static theory.

Usefulness of the proposed concepts

How can we use these notations that I propose?

I think they can be used as a very basic symbolic language to define problems. In some later stage they may be helpful in creating specific and practical methods of analysis.

I have used them so far as an aid in the planning of future studies at SIND.

In 1980 we made a long-run energy forecast for Sweden. In the analysis of the personal transportation sector, I made a table of items and developments and tried to identify those that are market-like (for instance the response of the consumer to higher petrol prices) and those that are process-like for instance the car stock, the car industry, technology.

Moreover, the exercise with different concepts showed that the market adjustments could be studied on different levels - the actual orientation of the transportation market in reality is not clear in a 'positivistic' sense.

I am now working on the problem of forest industry vs. wood burning. Attempting to construct a model framework of the problem, I found it useful to divide variables and concepts into one group of 'second dimension' concepts and one group in which the variables assumed values freely as in a multi-period model. World market prices and investment developments over a ten year period were sensed as 'development paths, while capacity use, timber felling, profitability in particular industries were treated as independent three-period variables.

The main reason for this is the need to economize on resources. One should not make all variables open in the sense of the multi-period model. We often make such mistakes, and the result is that the model itself takes command of the work.

September 1981
  (At  10th Nordic Congress on Operations Research, Oct 1981)

Gunnar Sommestad