Tests of Causal Measures

A causal measure is a number that represents the influence of a sequence of elements representing cause and effect in a model. The most common such sequence is a feedback loop. The measure would be one or more numbers representing the influence of that loop on variables in the model.

Loop impact is a measure of the influence of a feedback loop on the stocks in that loop. There are as many loop impacts as there are stocks in the loop. Thus, a third order loop has three loop impacts, one on each stock. Impact is defined between adjacent stocks only.

The concept of impact can be extend to exogenous influences, that is in circumstances where a loopis not formed. It is also possible to extend the definition of impact to the loop’s influence on flows.

For a measure of feedback loops and other casual links to be useful, it is suggested that they should obey two principles: continuity and additive. These principles can be expressed as tests of causal measures

Continuity Test

As the effect of a causal link (or loop) on a stock gets smaller, then the measure used for that causal link should tend to zero.

This test ensures continuity between the model with casual link or loop and the model without.

This test is illustrated with the three loop limits-to-growth model, figure 1. The stock x is subject to a growth mechanism, loop R0. The effects of this growth are limited by capacity M, loop B1. The third loop is a drain from x, loop B0, which causes the stock to fall short of capacity

Figure 1

To pass the continuity test then any measure of loop B0, for example, must get smaller as the effect of the loop on x is reduced so that in the limit of the loop vanishing the measure tends to zero. This test is passed for impact. Read the more in the Continuity Test of Causal Measures.

Additive Test

The measure of added causal links is the same regardless as to whether the links are added prior to flow entry, or they are added though multiple flows on the stock.

In any SD model, stock behaviour for the sum of the flows is the same as that for the flow of the sums. This result follows from the addition rule of integration. The sum of the integrals is the integral of the sums. Thus, any measure of the links for the sum of the flows must be the same as that of the flow of the sums.

For example the two models in figures 2 and 3 give identical behaviour for stock x. The only difference between them is that the two links from y and z are added together using separate flows in figure 2, but add directly before the flow in figure 3. To pass the additive test, measures for the effects of y and z on x must be the same in both models.

Figure 2
Figure 3

Impact passes this test. Read more in Additive Test of Causal Measures.