Loop Impact

The impact of one stock on another is a measure of how changes in a source stock cause changes in the motion of the target stock.

Let Y be a source stock influencing a target X. A change in Y will cause X to accelerate or decelerate, figure 1. This is the impact of Y on X.

impact

Fig 1. dx/dt = y

The impact of Y on X is measured by the acceleration imparted to X by Y, divided by the rate of change of X. Thus impact is a ratio that measures the curvature in the graph of X over time, figure 2. Constant impact would give an exponential curve.

impactgraph

Fig 2: dx/dt = y; x0 = 20; y0 = 0

Loop impact is the impact of the feedback loop on the behaviour of each stock in the loop. Specifically, this is the impact on the stock by the previous stock in the loop. For example, in figure 3 the impact of loop L on stock B is the impact of A on B.

loopimpact

Fig 3: Feedback loop with 4 stocks

The product of all the loop impacts in a feedback loop equals the loop gain, regardless of the complexity of the system dynamics model.

The causal connection between stocks can be interpreted as a  force in the Newtonian sense. Impact is then the ratio of the force to the momentum of the stock. See the Newtonian framework.