In certain northern European countries, parents used to tell their children that storks bring babies. For many years, I did not understand the actual link of how the old tale arose. However, I found out that in these countries that after a baby was born, the child’s nursery was frequently placed at the top of the house. Also, the parents would increase the heat within the house to keep the new born warm throughout the night. What happened is that the storks would discover these warmer roofs and would exploit this extra heat and would build their nests over the same rooms at the top of the house. So, the birth of the baby actually brought the storks and not the other way.

This amusing analogy can relate to causal vs non-causal models and well as an example with the idea of model dependency.

When constructing ERM models, if you know that situation A impacts situation B which again impacts situation C, you want your ERM model to reflect this causality. Usually a causal system is one that depends on current or past input only. If the the model depends on future values as well, you have an non-causal (or a-causal) model. Also see https://en.wikipedia.org/wiki/Causality for a further discussion around this topic.

However, when modeling various risks, initially, you may not be able to determine how different risks are properly interrelated. In these situations, you might use non-causal modeling to set up various statistical models to estimate a specific risk. Or you may set up a loose correlation model. In this situation, you know storks and delivery of babies are related so you would have a strong positive correlation.

Non-causal models with correlations were more frequently used before the financial crisis of 2008, primarily, because no one actually knew how to model credit. So, credit derivatives were modeled for several years, by setting up a VaR model and using copulas for the aggregation of risk. However, we saw that the relationship of the high quality bonds issues that were built off of the sub-prime mortgages and additional collateral was actually highly correlated in the extreme scenarios.

Now it is more common to create causal models where you design your scenarios and models to interrelate, which is the best approach. At least you would model the delivery of babies implying the arrival of storks.

However, in some companies, the non-causal models are still used, especially when that company wants to model a large diversity of risks. Also, if a company has several risks that are modeled separately with differing systems and scenarios, these risks may be segregated into silos. In these situations aggregation of capital may still require non-causal methods to handle the silos.

I think you need to dig in a little bit into why causal models are preferable and look at the limits of that preference. Non-causal models can be viewed as using proxy observations for unobservable variables to estimate an underlying causal model. I’ve been reading Optimal Control and Estimation by Robert Stengel and the book is broken into:

1&2. an introduction to dynamic systems,

3. optimal trajectories for fully deterministic systems and systems sufficiently smooth to not suffer from being treated as fully deterministic,

4. optimal estimation of system state for systems with deterministic mechanics but with unobservable variables,

5. optimal trajectories for stochastic systems combining both optimization of trajectories and estimation,

6. and a wrap-up with additional considerations for robust multi-variable control.

Causality doesn’t really come into play directly here other than being a signifier that there is an estimation element for both unobserved variables and underlying dynamics. I will say this is a bigger concern for actuaries than it is for engineers given that engineers have more capacity to control unobserved variables by controlling the environment immediately surrounding the system they are studying and they work on systems with shorter timescales allowing more observations to be made. But the overall playbook for engineers is very similar to the playbook for actuaries so this is still worth thinking about.

Causality may also sometimes steer you towards less efficient models if there are causally distinct mechanisms with immaterially different effects. If you think of a set of materially distinct plausible outcomes, it’s desirable you should be able to invert each outcome onto a set of model parameters that describes the outcome as the expected result. At the same time, it’s desirable that distinct but not materially different outcomes should be inverted onto a small set of parameter configurations. This property corresponds with the ability of the model to compress the range of possible outcomes. This property can also be viewed as an indicator that there is a homomorphism between the structure of the system and the structure of the model.

None of this should be regarded as a way of avoiding model specification error. That can’t be avoided. The best defense against model specification error is documenting how the model was specified and the alternatives that have been considered. For one, having good explanations of what you are doing should reduce the risk of the error and two, communicating that actions that are mistakes in hindsight had defensible rationales at the time has social value.