November 2018

System Dynamics Modeling

By Carlos Fuentes

This short article is based on “Making Sense of the Unexpected” published in The Actuary, Dec 2017/Jan 2018, where the reader can find a fuller description of system dynamics (SD) and suggested readings.

PROBABILISTIC AND STATISTICAL MODELS

Typically, business forecasts are heavily dependent on statistics. While statistics are reliable in many circumstances such as short-term forecasting, life insurance and pension analysis, statistical forecasting doesn’t capture the dynamics of complex environments because one of its key assumptions—that historical conditions are a valid proxy of future behavior—may not be satisfied. Because these techniques—almost always a form of regression—are not designed for long-term predictions nor necessarily to understand how variables interact, they can misrepresent causation and correlation. Here are a few examples [1]:

• Ice cream consumption leads to murder
• A pirate shortage caused global warming
• Using Internet Explorer leads to murder
• Mexican lemon imports prevent highway deaths
• Obesity caused the debt bubble
• Facebook caused the Greek debt crisis

The implausibility of causation in these time series protects us from reaching absurd conclusions.  But there are instances where common sense cannot be invoked as a safeguard against absurd outcomes. If the correlation coefficient between {xi} and {yi} is significant and little is known about the nature or behavior of these series it is difficult to ascertain whether the correlation is real or spurious. Even if {xi}and {yi} are correlated at some point in time they may evolve (as medical claims do) rendering any past relationship (say between a prescribed drug and expected costs) useless. Surprisingly, many predictive models assume that time series are not (time) dynamic and, perhaps more strikingly, some practitioners subscribe to the idea that a model that “predicts” the past can forecast the future.

SYSTEM DYNAMICS

Fortunately, there are modeling techniques that are better suited to understand cause-effect relationships. SD is one of them. In SD, interconnections between components, especially those that lead to feedback (whereby an action eventually leads to more changes in the same lever), play a central role. Time delays are also properly represented. If you understand the problem, you can model it. If you model it but results are illogical, then your knowledge of the system is incorrect. But as you improve it, your understanding of the problem improves.

To illustrate: as medical technology advances, people live longer, so population increases. As population grows, the demand for medical technology is fueled, which creates more revenue to further improve medical technology. This is called reinforcingfeedback because the original action (improvement in medical technology) is eventually increased, i.e., reinforced.

In another example, as reinsurers compete they reduce premium rates. Eventually premium collected won’t be enough to cover losses and make a profit. The natural reaction is to raise prices until business becomes profitable again, a process that can take years. But once this goal is achieved, reinsurers start competing to gain market share. The process repeats itself as reinsurers try to capture market share and be profitable. In the lexicon of SD, reinsurers try to keep the system near its goal through a balancing feedback mechanism.

An SD model mirrors the workings of reality as much as is reasonable but purposefully leaves out irrelevant details that complicate the model without improving it and, frequently, make it less robust.

CONCLUDING REMARKS

Perhaps the greatest strength of SD is its emphasis in understanding how complex systems work, what matters, what does not, and how levers interact. If you understand the problem, you can model it. If you model it, but simulations or predictions are incorrect, then your understanding is deficient. When this happens, as you improve the model, your knowledge of the system is enhanced and you gain strategic insights.

Carlos Fuentes, FSA, MAAA, MBA, MS, is president of Axiom Actuarial Consulting. He can be reached at carlos-fuentes@axiom-acturial.com.

1  See “The 10 Most Bizarre Correlations” in https://www.buzzfeednews.com/article/kjh2110/the-10-most-bizarre-correlations