Chapter 4: The Art of Causal Modeling
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Chapter 4 The Art of Causal Modeling Fashion models and financial models are similar. They bear a similar relationship to the everyday world. Like supermodels, financial models are idealized representations of the real world, they are not real, they don’t quite work the way that the real world works. There is celebrity in both worlds. In the end, there is the same inevitable disappointment. Satyajit Das, Traders, Guns & Money: Knowns and Unknowns in the Dazzling World of Derivatives Essentially, all models are wrong, but some are useful. G. E. P. Box and N. R. Draper, Empirical Model Building and Response Surfaces In the HP definition of causality, causality is relative to a causal model. X = x can be the cause of ϕ in one causal model and not in another. Many features of a causal model can impact claims of causality. It is clear that the structural equations can have a major impact on the conclusions we draw about causality. For example, it is the equations that allow us to conclude that lower air pressure is the cause of the lower barometer reading and not the other way around; increasing the barometer reading will not result in higher air pressure. But it is not just the structural equations that matter. As shown by the Suzy-Billy rockthrowing example (Example 2.3.3), adding extra variables to a model can change a cause to a non-cause. Since only endogenous variables can be causes, the split of variables into exogenous and endogenous can clearly affect what counts as a cause, as we saw in the case of the oxygen and the forest fire. As a number of examples in Chapter 3 showed, if we take normality considerations into account, the choice of normality ordering can affect causality. Even the set of possible values of the variables in the model makes a difference, as Example 2.3.7 (where both the sergeant and captain give orders) illustrates. Some have argued that causality should be an objective feature of the world. Particularly in the philosophy literature, the (often implicit) assumption has been that the job of the philosopher is to analyze the (objective) notion of causation, rather like that of a chemist analyzing 107 108 Chapter 4. The Art of Causal Modeling the structure of a molecule. In the context of the HP approach, this would amount to designating one causal model as the “right” model. I do not believe that there is one “right” model. Indeed, in the spirit of the quote at the beginning of this chapter, I am not sure that there are any “right” models, but some models may be more useful, or better representations of reality, than others. Moreover, even for a single situation, there may be several useful models. For example, suppose that we ask for the cause of a serious traffic accident. A traffic engineer might say that the bad road design was the cause; an educator might focus on poor driver education; a sociologist might point to the pub near the highway where the driver got drunk; a psychologist might say that the cause is the driver’s recent breakup with his girlfriend. Each of these answers is reasonable. By appropriately choosing the variables, the structural-equations framework can accommodate them all. That said, it is useful to have principles by which we can argue that one model is more reasonable/useful/appropriate than another. Suppose that a lawyer argues that, although his client was drunk and it was pouring rain, the cause of the accident was the car’s faulty brakes, which is why his client is suing GM for $5,000,000. If the lawyer were using the HP definition of causality, he would then have to present a causal model in which the brakes were the cause. His opponent would presumably then present a different model in which the drunkenness or the rain was a cause. We would clearly want to say that a model that made the faulty brakes a cause because it did not include the rain as an endogenous variable, or it took drunkenness to be normal, was not an appropriate model. The structural equations can be viewed as describing objective features of the world. At least in principle, we can test the effects of interventions to see whether they are correctly captured by the equations. In some cases, we might be able to argue that the set of values of variables is somewhat objective. In...