Some Properties of Positive Feedback Models and Some Examples

K. Bertels & L. Neuberg


FUNDP - University of Namur

In this brief position paper, we want to look at some theoretical properties of a particular category of models and see to what extent they are applicable to problems of structural change. More specifically we will look at the properties of self reinforcing mechanisms or positive feedback systems as opposed to diminishing returns and negative feedback where the system evolves to a single and stable equilibrium. Positive feedback systems (`positive' should not be interpreted as `good' but in the sense of a catalytic influence) give rise to a specific kind of behavior.

Even though other authors have made significant contributions, it is the credit of Brian Arthur to have formalized this idea of positive feedback in the form of non-linear Polya processes. Arthur restricts his approach to high-tech industries and how markets come to choose for a particular technology rather than another. However we will try to apply his ideas to issues of structural change. By structural change we mean any change in structure of an national economy, a commercial organization or any other system (financial market, ...). Applying here simply means looking for examples that, at first sight, bear some resemblance to the discussed properties. We therefore do not claim that positive feedback models are completely applicable to the kind of phenomena described. The following should be seen as a Gedankenexperiment and could serve as a basis for discussion.

Non-ergodicity or path dependence

Ergodic systems are characterized by the fact that any future event is completely independent of whatever event has happened in the past. So, the probability of an event to happen in the future is not influenced by past experiences. In a way, we could translate this as the incapability to learn. Non-ergodic systems are of course the opposite because there the probability of a future event is influenced if not determined by previous experiences. We also call this path dependence and such systems could be viewed as being able to learn.

Unpredictability

Positive feedback systems, from a theoretical point of view have multiple possible equilibria. An equilibrium is an endstate to which a system can evolve and in which it then remains unless something happens that disturbs the equilibrium. We make the distinction between stable and unstable equilibria (also called fixed points). An equilibrium is said to be stable if a small perturbation does not cause the system to leave the equilibrium state. It is unstable if this small perturbation does not cause the system to go into a different state. In positive feedback systems, it is impossible to predict to which equilibrium the system will evolve. This is due to the fact that small, and apparently insignificant random events may push the system to a particular fixed point.

Non superiority and non optimality

As we have multiple equilibria, the problem would be easy if one of them would be clearly superior and to which the system would always be attracted. This does not necessarily mean that all possible equilibria are of equal quality but only that the probabilities of reaching any equilibrium are the same. This is of course related to the fact that small events can change the outcome of the system and it is difficult to predict or influence these events. This also implies that not necessarily the best or optimal (e.g. technological) solution will be adopted by the system.

Sensitivity to Initial Conditions

A notion closely related to the previous ones is sensitivity to initial conditions. We have spoken about the small random events that can determine the final outcome of the system. This also means that two systems (national economies with similar structures, comparative advantages, etc.) who are only marginally different (in this case people taking slightly different decisions based on different perceptions or preferences) will follow a radically different path and will consequently (given the path dependence) end up in a different state (fixed point or equilibrium). It is this sensitivity to initial conditions that renders systems unpredictable because it is impossible to have the full information on all the state factors of the system.

Emergent Rationality

A final characteristic that has to do with the global behavior of a system could be called emergent rationality. We can describe the components of a system in terms of behavior, structure and the way these components can interact. However, what cannot be predicted in a number of situations is what the overall behavior will look like. There appears to be some discontinuity between the micro and macro level. Generally, it is said that this is due to the non-linear local interaction of the constituing elements (also called agents). Nowhere is the global behavior explicitly defined but it does display some kind of rationality, therefore called emergent rationality.

Some Examples:

A first example is a quote from one of the articles by Arthur. `For example, in the early 1970s, Japanese automobile makers began to sell significant numbers of small cars in the United States. As Japan gained market volume without much opposition from Detroit, its engineers and production workers gained experience, its costs fell and its products improved. These factors, together with improved sales networks, allowed Japan to increase its share of the U.S. market; as a result, workers gained still more experience, costs fell further and quality improved again. Before Detroit responded seriously, this positive feedback loop had helped Japanese companies to make serious inroads into the U.S. markets for small cars. Similar sequences of events have taken place in the markets for television sets, integrated circuits and other products.' [Arthur 90]

A second example discusses the transformation of Eastern Europe. Again we take some quotes this time from an article by Wyplosz. It illustrates the fact that even though there are theoretical reasons to assume a system will evolve in a specific way, small or relatively unimportant events cause reality to diverge from theory.

`During the course of 1989, there was a widely shared feeling of enthusiasm as formerly planned economies in Europe announced their determination to embrace the market system. It was expected that the shift would take the shape of a J-curve. After an early, possibly deep and longlasting recession, fast growth would set in and allow CEE, within a decade or two, to catch up with Western Europe ... Three years later, a deep sense of disappointment, sometimes even failure is developing among a number of observers. To varying degrees, measured output has fallen dramatically, unemployment is quickly rising above Western European levels, inflation which initially exploded is still not under control and budget deficits deepen...
The addition of minority discontents may result in major political difficulties and this leads governments to avoid actions that generate strong minority objections... There is a need therefore to pay attention to such `details' as political acceptability.' [Wyplosz93]

The third example also comes from the same area, namely the transformation of Eastern European economies. This time we give a quote from an article by van Wijnbergen who gives two reasons, both of them related to micro-behavior, that at an aggregated level lead to unexpected results.

`How should prices be decontrolled, slowly or in a big bang? Why is it that governments committed to eventual price flexibility so often seem to be unable to let go of `temporary' controls? How can one explain that after price increases early in a programme of price controls, output often rises while at the same time shortages also increase? This paper argues that intertemporal speculation, hoarding and the political economy of price reform go a long way towards explaining all these puzzles. We show that the interaction between shortages and political vulnerability of reformist governments to early perceptions of failure make for a strong argument against gradualism in the decontrol of prices...
Price controls often focus on commodities that are storable and can thus be used in intertemporal speculation... The smaller the initial price increase, the lower the observed supply eleasticity and the greater the probability that the programme of reform will be abondoned' [Wijnb92]

A final example focuses more on organizational and decision making change in companies due to the introduction of new technology, hand held computers in this case. Again it illustrates the fact that relatively small changes can have a dramatic impact on the overall organization and the way it functions.
`For example, the U.S. textile industry has begun implementing a series of electronic connections among companies as part of the Quick Response Program... these electronic connections link companies all along the production chain, from suppliers of fibers (such as wool and cotton) to the mills that weave these fibers into fabric, to the factories that sew garments and , ultimately, to the stores that sell the garments to consumers. When such networks are fully implemented, they will help companies respond quicker to demand. For instance, when a sweater is sold in New York City, a scanner reading the bar-coded label may automatically trigger ordering, shipping and production activities all the way back to the wool warehouse in South Carolina. This new, multiorganizational structure will reduce inventory costs every year' [Malrock95]

Conclusion

We have tried to illustrate that the theoretical framework of positive feedback does constitute an interesting tool for modelling and describing (not predicting!) a wide variety of phenomena outside the realm of high-tech products. We have done this in an informal way by simply quoting from articles hoping that the reader can find the more theoretical characteristics in each of the examples. If we are able to do that, then a plausible but also very cautious conclusion could be that computer models used for simulation should include this kind of behavior and should therefore be able to reproduce characteristics such as path dependence and sensitivity to initial conditions.

Bibliography

Arthur, B., Increasing Returns and Path Dependence in the Economy, University of Michigan Press, 1994, 201 p.

Malone W., Rockart J.F., Computers, Networks and the Corporation, Scientific American, special issue 1995, pp. 140-147

van Wijnbergen S., Intertemporal speculation, shortages and the political economy of price reform, The Economic Journal 102, November 1992, pp. 1395-1406

Wyplosz Ch., After the honeymoon. On the economics and the politics of economic transformation, European Economic Review 37, 1993, pp. 379-386