4.2.1 Interventions on heterogeneous variables

X is a heterogeneous variable with respect to Y if X’s obtaining value x can be realized in multiple ways such that different ways of setting X to x by interventions result in significantly different probability distributions of Y, even when the interventions are assumed to be ideal.Footnote ⁵ In this case, interventions on X with respect to Y will be ambiguous because CE(X, Y) is ill-defined. More specifically, a variable X can be heterogeneous with respect to Y at least in the following two ways: (1) X is an aggregation of several variables with differential effects on Y; and (2) the effect of X on Y differs in different units or contexts.Footnote ⁶

In practice, we do not always know beforehand whether X is heterogeneous. We might first find out that interventions on X are ambiguous and then diagnose the ambiguity as a consequence of using heterogeneous variables. For example, imagine that back in the 1950s, we did not know the components of total cholesterol, and different studies reported inconsistent results about the effect of TC on HD. One plausible explanation for this inconsistency would be that TC was a heterogeneous variable.

Both types of heterogeneity mentioned in the preceding text imply that high-level or population-level variables are more likely to be heterogeneous. But this does not mean we should always choose variables that are as fine-grained as possible. Coarse-grained variables have their advantages. For example, they reveal causal patterns that cover a broad range of phenomena, they can simplify causal models, they are easier to measure, and so on. Therefore, in practice, there is usually a trade-off between the reduction of heterogeneity and other goals in variable choice. When the heterogeneity is within reasonable limits, we need not have to abandon the variable.

Suppose the heterogeneity in an aggregated variable X (= X ₁ + X ₂) with respect to Y does exceed a reasonable degree. In this case, the association between X and Y no longer supports causal interpretation, and we should use {X ₁, X ₂, Y} as our new causal variables. Note that the (spurious) association between X and Y is not a consequence of confounding and cannot be eliminated by blindly applying confounding adjustment—not all systematic spurious associations are results of confounding. Sometimes they are brought about by poor variable choice and can only be eliminated by reselecting our variables.

To make the preceding point clearer, in Figure 2(a), I draw a causal graph in which X and {X ₁, X ₂} are included in the same causal model (double arrows between X, X ₁, and X ₂ represent noncausal relations). In this graph, it makes no sense to disambiguate the intervention on X by holding X ₁ fixed because the intervention will then collapse into an intervention on X ₂. That is, holding X ₁ fixed is in effect replacing X with {X ₁, X ₂}.

Figure 1. An ideal intervention I on X with respect to Y breaks the arrow going into X.

Another way X can be heterogeneous is when X’s obtaining the same value can affect Y differently in different units or contexts. The situation can be represented schematically in Figure 2(b).Footnote ⁷ In this graph, Z is a set of factors responsible for the heterogeneity in CE(X, Y). This kind of heterogeneity is related to the well-known fact that how X affects Y often depends on or interacts with the context or background factors (e.g., whether a drug can relieve my headache depends on various characteristics of mine).Footnote ⁸ Probably all high-level causal variables are more or less heterogeneous in this sense. It is virtually impossible for causal effects in the high-level sciences to remain consistent in all contexts. Luckily, the problem is not as serious as it appears.

Figure 2. Two kinds of heterogeneity in CE(X, Y). (a) (Left) X is an aggregation of X ₁ and X ₂ with different effects on Y. (b) (Right) Background factors Z (which may differ in different units) are responsible for the heterogeneity.

In many cases, CE(X, Y) is still reasonably homogeneous in the “normal” or “average” causal contexts. X and Y can be perfectly legitimate causal variables if they are used in these contexts. Moreover, we may also be able to reduce the heterogeneity by holding variables in Z constant (e.g., by studying units with similar levels of Z). The moral is that although the effects of higher-level variables tend to be heterogeneous due to context-dependency, many of them still describe robust properties of the world and can be useful in causal inference.

Consider biodiversity. According to McCann (Reference McCann2000), observations show that diversity tends to be positively correlated with ecosystem stability in an ecosystem. However, as McCann emphasizes, this association does not mean that diversity is the “driver” of ecosystem stability; that is, this association does not support a causal interpretation. This is because biodiversity is an abstract characteristic of an ecosystem that does not consider other factors that may contribute to stability, such as underlying interactions between species. Two habitats may have the same level of biodiversity but differ significantly in their modes of species interactions and hence differ in their levels of stability. As a result, attempts to manipulate ecosystem stability by manipulating biodiversity may fail if we ignore other relevant factors. Nevertheless, despite the previously mentioned problem, biodiversity may still be seen as a well-defined cause of stability if we focus on ecosystems with roughly similar modes of species interactions. We may also successfully manipulate ecosystem stability by manipulating biodiversity if species interactions and other relevant factors are maintained at a fixed level.

4.2.2 Interventions on ontologically controversial variables

Consider the following situation: CE(X, Y) is ill-defined because we cannot tell a univocal underlying story about how ideal interventions on X with respect to Y work. For example, suppose, according to one plausible understanding, X supervenes on (or is defined by) variables X={A, B, C}, and therefore, an intervention on X is just an intervention on variables in X. But according to another plausible understanding, X supervenes on X*={A, B} (see Figure 3). In this case, an intervention on X is just an intervention on X*. It follows that an ideal intervention on X does not have a determinate underlying causal mechanism. Now, if C has a significant effect on Y, it follows that CE(X, Y) is ill-defined. Any intervention on X with respect to Y will then be ill-defined.

Figure 3. Causal graphs in which X supervenes on a set of lower-level variables. (a) (Left) The supervenience base is X = {A, B, C}; (b) (Right) The supervenience base is X* = {A, B}.

This kind of ambiguity occurs when the concept used to construct X is conceptually contested, and this problem is especially severe in the social sciences. It is widely recognized that social categories are prone to conceptual disputes: They often have unclear boundaries and their boundaries may even change over time (see Greene Reference Greene2020 on how this may have an impact on the choice of causal variables in the social sciences); moreover, classifications of social groups can affect how people behave (the so-called looping effects). In particular, for many social characteristics, there can be different conceptions of them that are all, to some extent, plausible, and it is unlikely that philosophers and social scientists can achieve agreement on what these characteristics “really” are. This raises the question of whether ideal interventions on them are sufficiently univocal. Importantly, the issue here is not that we lack knowledge about these characteristics (although this is not to say empirical evidence is irrelevant to this issue). The controversies over them are primarily ontological rather than epistemic.

Take “race” as an example.Footnote ⁹ It is still heatedly debated what race is—whether race is biologically grounded, socially constructed, or a bit of both (James & Burgos Reference James and Burgos2020). An ideal intervention on race may mean different things based on how one conceives of race. Here, I will not take a stance on how we should understand race. For my discussion that follows, it suffices to acknowledge that so far we do not (and probably never will) have a consensus on the ontological status of race.

Let us start with the suggestion that race can be biologically defined, and thus we can manipulate one’s race through genetic engineering. We should immediately notice the biological indeterminacy involved in such a manipulation. Unlike sex, which is normally determined by the sex chromosomes, genetic variations between different human races and within each human race are far more complicated. There is probably no shared set of alleles that can unequivocally identify a particular race. Worse, the genetic variation within each race may be even larger than the average variation between races. Therefore, it is difficult to determine which genes to modify when conceiving an ideal intervention on race. This will lead to ambiguities in interventions on race because manipulating different sets of genes may have quite different effects on the outcome of interest.

Partly due to the preceding considerations, many people contend that race is not a well-defined biological category. If they are right, merely manipulating genetic factors is not a manipulation of race per se, but, at best, a manipulation of typical biological characteristics associated with race. An intervention on race needs more than this. If belonging to a racial group means receiving a particular kind of cultural upbringing, a manipulation of a Black girl’s race should also change her cultural upbringing as well. For example, Marcellesi (Reference Marcellesi2013) suggests that to manipulate race, besides genetic factors, we should also change environmental factors (e.g., who will be the mother of an embryo).

Another controversy concerns whether race is, by definition, genealogical. If race is not genealogical, a manipulation of a Black girl’s race has nothing to do with her ancestors’ race. In this case, given that her ancestors’ race is a cause of her race, the manipulation will simply break the arrow from her ancestors’ race to her race. Alternatively, one may contend that race is genealogical (e.g., one may say, for a person to be Black, at least one of their parents should be Black). In that case, an intervention on the girl’s race will simultaneously be an intervention on her ancestors’ race because what we have here is a definitional relationship between these variables. Consequently, depending on whether one thinks race is genealogical, an ideal intervention on race can have quite different causal structures.

I believe the preceding discussion suffices to show that, by default, we should avoid using race as a cause. Those who do not want to accept this conclusion are obliged to provide a way to disambiguate the concept of race so as to reduce the ambiguity in interventions on race. A straightforward way to do so is to consider a well-controlled, idealized scenario. Consider the following argument from Marcellesi (Reference Marcellesi2013). Suppose in an imaginary society, there are two racial groups, A and B. All the individuals in the population are perfectly homogeneous regarding possible causes of wages other than race (e.g., education and working experience). Now suppose A-group is much less likely to get high-wage jobs than B-group. The only cause of this wage gap, Marcellesi argues, is race.

Marcellesi’s argument relies on constructing a highly idealized scenario in which conceptual or ontological disputes over race no longer exist. In this scenario, whether a person belongs to a racial group is a standalone fact that does not depend on other properties of this person since everyone is otherwise similar. However, even if we grant that in this imaginary scenario, race is a cause, the argument’s relevance to a realistic society is unclear. In our society, different racial groups are heterogeneous in various properties, which is precisely why it is so hard to define race. The realistic concept of race is thus quite different from the one in Marcellesi’s imaginary society. The upshot is that the concept of race may be inherently ambiguous so that if we try to make race a well-defined cause by idealizing its context of use, it could turn out that this simplified concept of “race” is no longer the one we are really interested in.

Holland (Reference Holland, Zuberi and Bonilla-Silva2008) also argues against using race as a causal variable, but I disagree with him on the rationale behind his assessment: He thinks race is not a cause because, as an attribute, race cannot be manipulated in the way we manipulate a treatment. Indeed, by restricting the realm of causes to treatments, the kind of ambiguity we find in social attributes like race will disappear because there are rarely conceptual or ontological disputes over the nature of a treatment (which is typically defined operationally). However, as I have argued earlier, the limitation of this strategy is also severe: It not only rules out race as a cause but also any variable that describes an attribute, regardless of whether such an attribute is ontologically controversial.

In response to Holland (Reference Holland, Zuberi and Bonilla-Silva2008), Marcellesi (Reference Marcellesi2013) contends that race can be used as a treatment: We can randomly assign race to embryos because we can assign biological factors (using genetic engineering) and environmental factors (by swapping embryos between mothers) to embryos. I suspect that this is a misunderstanding of the notion of “treatment” (see my discussion in section 3.2). Here, it seems what is being assigned as a treatment to an embryo is not race, but the procedure of genetic engineering and the embryo’s upbringing.

4.2.3 Interventions that are ham-handed (aka fat-handed)

Consider the intervention I that is shown in Figure 4. It affects Y through an additional causal path that does not go through X. The association we observe between X and Y under this intervention is not identical to CE(X, Y). This intervention is hence ham-handed (aka fat-handed).

Figure 4. I is a ham-handed intervention on X. (a) (Left) I is a direct cause of Y. (b) (Right) Z is an intermediate variable between I and Y.

Hernán and Taubman (Reference Hernán and Taubman2008) state that ham-handed interventions are not WDIs. When interventions are ham-handed, two different methods of manipulating X may lead to different distributions of Y if, in the two methods, the effect of I on Y via the ham-handed causal path (or the “side effect” of I) differs significantly. Consider interventions on obesity. We can conduct two trials in which we manipulate the level of obesity from high to low but in different ways—through physical exercise and diet control, respectively. According to Hernán and Taubman, these two manipulations of obesity will lead to significantly different mortality outcomes because the side effects differ in the two studies; the mortality rate will be lower in the first trial. To them, this means that interventions on obesity violate the consistency requirement. Interventions on obesity are, therefore, not WDIs. Hernán and Taubman (Reference Hernán and Taubman2008, 513) conclude, “if the goal is to inform policy, it may be better to focus on modifiable lifestyle behaviors than on obesity itself.”

Hernán and Taubman’s preference for lifestyle variables is certainly well-motivated in certain respects. Lifestyle behaviors like physical exercise and diet control can be used as treatments in experiments, and interventions on treatments are designed to be non-ham-handed because there is no additional causal path going from a treatment assignment to the outcome of interest. Therefore, interventions on lifestyle behaviors are more likely to generate consistent results across different studies. In contrast, nontreatment variables like obesity are more likely to lead to “inconsistencies” between studies. In this respect, lifestyle behaviors are indeed better causal variables.

Nevertheless, their argument does not constitute a well-grounded objection to using obesity as a causal variable. Even if obesity is an inferior variable in certain respects, it has its own advantages, which should be taken into account in one’s choice of causal variables, together with its disadvantages. First, obesity supports more general causal claims and causal estimations. This makes it possible to generalize results from various studies on the effects of diet control and exercise and predict the consequences of a broad range of specific behavioral causes. For example, if we want to predict the overall mortality trend in a country in the next few decades, it may be better to look for a few causes such as obesity, hypertension, and so on, instead of a larger number of behavioral causes.

Moreover, although it might be true that variables like diet and exercise are more useful for policy making, these variables cannot fulfill our epistemic interests in the effects of biological characteristics. As a matter of fact, both the public and scientists are interested in the effects of obesity. In particular, when the goal is explanation, obesity or adiposity may be a better candidate for explaining health outcomes because obesity is often a more proportional cause than lifestyle behaviors. This is also true for many other biological characteristics. Besides, it is worth mentioning that Pearl (Reference Pearl2018) makes a similar argument by emphasizing the distinction between “policy-based” and “scientific” causation.

Even for purposes of policy making, understanding the effects of obesity can still be important. If obesity is an important intermediate variable between lifestyle behaviors and deaths, specifying the causal pathways may help us achieve a better understanding and estimation of how lifestyle behaviors affect mortality. Finally, because the prevalence of obesity is easier to measure and monitor compared to the prevalence of unhealthy lifestyle behaviors, the former may turn out to be more useful for purposes of improving public health.

There is yet a more severe problem with Hernán and Taubman’s reasoning. Granted that interventions on obesity may report “inconsistent” results between different studies, it is important to further identify the source of the inconsistency. If the source is in the inconsistency of the effect of obesity on mortality, then it probably means we should abandon obesity as a causal variable. But if the inconsistency can be entirely attributed to the ham-handedness of interventions, such an apparent “inconsistency” does not necessarily mean obesity is a bad causal variable. In the latter case, what we should do is ask whether it is possible to identify CE(Obesity, Mortality) from these ham-handed interventions through some indirect methods.

Whether obesity has consistent effects on health outcomes under conceivable ideal interventions is a question that is not touched on by Hernán and Taubman. This question involves empirical issues about the physiology of human adipose tissue, especially how excessive white adipose tissue leads to diseases (this is an ongoing area of research; see Cypess Reference Cypess2022 for a review). If it turns out that causal pathways from white adipose tissue to health outcomes are significantly heterogeneous, this suggests that CE(Obesity, Mortality) is ill-defined. I am not trying to do armchair physiology here. What I want to emphasize is that nothing in Hernán and Taubman’s discussion supports that CE(Obesity, Mortality) is ill-defined.

Assuming that CE(Obesity, Mortality) is well-defined, there is still the question of whether we can reliably identify this effect from ham-handed interventions. Hernán and Taubman seem to assume that we cannot. But there remains a possibility that we can identify CE(Obesity, Mortality) if we can eliminate or reduce the bias induced by the ham-handed path. For example, there may be available data on the direct effect of exercise (or diets) on mortality that does not go through obesity such that we can deduct the side effect. However, if there is a mediator Z on the ham-handed path from intervention I to outcome Y, as shown in Figure 4(b), we can then adjust for Z to eliminate the bias.

Of course, these are merely theoretical possibilities; it may turn out that, in practice, there are no reliable ways to identify CE(Obesity, Mortality) from the data to which we have access. In that case, Hernán and Taubman would still be justified in claiming that interventions on obesity are ill-defined. But this will not invalidate the key point I have made; namely, we should distinguish between the case in which CE(X, Y) is inconsistent and that in which different studies report apparently inconsistent results because interventions used in these studies are ham-handed (or nonideal). In the latter case, ham-handedness can simply be seen as a new source of bias in causal inference. Ham-handedness does not immediately suggest that the variable being manipulated is unsuitable for being a cause.