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|mechanism schema is a representation of a set of mechanisms in which some known details (or known nested levels) are suppressed for the sake of simplicity. Or, as Machamer, Darden, and Craver (2000:15) state, a mechanism schema is a truncated abstract description of a mechanism that can be filled with descriptions of known component parts and activities. In contrast, a mechanism sketch is quite different:|
A sketch is an abstraction for which bottom out entities and activities cannot (yet) be supplied or which contains gaps in its stages. The productive continuity from one stage to the next has missing pieces, black boxes, which we do not yet know how to fill in. A sketch thus serves to indicate what further work needs to be done in order to have a mechanism schema. Sometimes a sketch has to be abandoned in the light of new findings. In other cases it may become a schema, serving as an abstraction that can be instantiated as needed .... (Machamer, Darden, and Craver 2000:18)
Within this framework, one can conceive of causal analysis in the social sciences as the pursuit of explanations that bottom out.18 Although there will inevitably be differences of opinion on how deep an explanation must be to bottom out, it would seem uncontroversial to state that a valid explanation that invokes a mechanism must bottom out at least as far as the observables in the data at hand.19
Now, consider the application of this framework to the sort of causal diagrams we have considered so far. Suppose that one uses some form of back-door conditioning to identify a casual effect of on . Suppose, furthermore, that one has done so from within the counterfactual framework, settling upon the average causal effect as the parameter of first-order interest. One then necessarily confronts the question that we raised in the beginning of this chapter: Does a counterfactually-defined and consistent estimate of the causal effect of on by itself meet the standard of an explanation that bottoms out?
The answer to this question is clearly: It depends on what and are, who is conducting the study, and for what purposes. If one wishes to know only how a hypothetical intervention on would shift , and hence has no interest in anything else whatsoever, then bottoming out has been achieved in some minimalist way. The analysis yields up a consistent estimate of the average causal effect of on that holds for the population within which both are observed. In this case, the model is then regarded as merely a mechanism sketch, which suffices to be treated as a sufficiently deep explanation for the purposes at hand.
However, as we have noted from the beginning of this chapter onward, it will often be the case that an estimate of a warranted causal effect of on , grounded in the potential outcomes framework, is properly considered to be an insufficiently deep explanation of how brings about . Such a judgment would be appropriate when the interest of the field is in understanding both how interventions on and interventions on the mechanistic intervening variables that link to would shift . In this case, the model is a mechanism sketch that, for the purposes at hand, cannot be regarded as a sufficiently deep explanation. The arrow in the sketch is a black box that must be filled in through further analysis.
If a warranted claim of a counterfactually defined causal effect is properly regarded as insufficiently deep, the recourse is not to abandon the counterfactual model, but rather to investigate the nested mechanism that intercepts the effect of on . Such analysis may initially take the form of a set of alternative conjectured mechanisms. But, ultimately, any such analysis must return to the particular observed relationship between and in the population of interest (or more broadly in multiple well-defined populations for which the question of interest is relevant). Thus, although theoretical creativity may be required, opening up black boxes is, at least in part, an empirical pursuit. At some point, one must specify the counterfactual states for the variables that constitute the mechanisms, and each link thereby specified must be submitted to its own causal analysis.
Consider this process abstractly with reference to a causal diagram, after which we will introduce a real-world example. Suppose that one pursues further theoretical conjecturing and subsequent empirical analysis, and one then determines that the variables , , and constitute an isolated and exhaustive mechanism that identifies the causal effect of on via Pearl's front-door criterion. At this point, one may be tempted to declare that a sufficiently deep causal explanation of the effect of on has been secured. Such a claim may well be true, but it is not guaranteed. It could be that there are further nested mechanistic variables, such that, for example, three additional variables , , and (each of which is a concept of considerable interest to one's peers) are then found to mediate the casual pathway . In this case, the casual pathway is then itself best regarded in hindsight as merely a component of a mechanism sketch. When , , and are then observed, is replaced in the mechanism sketch with, for example, one or more related causal pathways, such as and . In this example, , , and may well identify the causal effect by the front-door criterion, but they do not qualify as a sufficiently deep causal account of how brings about .
As we noted in the first part of this chapter, the progressive deepening of causal explanation through the modeling of intervening processes is entirely consistent with social science tradition. And yet, we also claimed that Pearl's front-door criterion can help guide sharpened analysis practices in this regard. To see what we mean, consider the example of Duncan's research on status attainment processes again. As we noted earlier, Blau and Duncan (1967) deepened the causal account of how parental social status determines offsprings' social status by specifying what most scholars now regard as the most important link: levels of educational attainment.
Thereafter, Duncan and his colleagues then supported and encouraged further work on the process of educational attainment, most importantly the Wisconsin model of status attainment that we introduced earlier in section Ex: Background and intelligance on education. This model is a direct extension of Blau and Duncan's research, in which the causal pathways between parental status and offspring's attainment were elaborated by the introduction of intervening variables for significant others' influence and educational aspirations. In fact, in the most important article in this tradition, Sewell, Haller, and Portes (1969) use mechanistic language to introduce the contribution of their study:
... we present theory and data regarding what we believe to be a logically consistent social psychological model. This provides a plausible causal argument to link stratification and mental ability inputs through a set of social psychological and behavioral mechanisms to educational and occupational attainments. One compelling feature of the model is that some of the inputs may be manipulated through experimental or other purposive interventions. This means that parts of it can be experimentally tested in future research and that practical policy agents can reasonably hope to use it in order to change educational and occupational attainments. (Sewell et al. 1969:84)
The Wisconsin model was very favorably received in sociology, as it was considered to be consistent with the basic features of the model of Blau and Duncan (1967) and yet had a claim to greater causal depth.
Even so, as we also noted in section Ex: Background and intelligance on education, critics emerged immediately (see also Morgan 2005, Chapter 2 for a more extended summary). The basic argument was that, even if significant others' influence and educational aspirations have causal effects on educational attainment, they are both grounded in part in sources outside of parental status and mental ability (a point the authors of the Wisconsin model recognized). Thus, although significant others' influence and educational aspirations may be helpful to some extent in offering an interpretation of some of the causal process that generates intergenerational correlations of educational attainment, these intervening variables do not qualify as an isolated and exhaustive mechanism that fully accounts for the effects of parental status on offsprings' status.
In this regard, the Blau and Duncan model can be regarded as a mechanism sketch for the status attainment process, and the Wisconsin model can then be regarded as the first mechanism-based attempt to deepen its implied explanation. The Wisconsin model was therefore an important step forward, but it was not conclusive and did not settle all further research.
Nearly forty years later, it is now clear that the Wisconsin model itself is a mechanism sketch. The research community of inequality scholars in sociology seems to have concluded that its pathways have not bottomed out, and much research continues on the processes that generate educational aspirations (as well as whether or not the relationship between aspirations and attainment is sufficiently explanatory to be useful). Moreover, some scholars (e.g., Goldthorpe 2000) have produced entirely different mechanism sketches for the relationship between parental status and educational attainment. The future of this research tradition is clearly careful empirical analysis that can adjudicate between these rival mechanism sketches, which will only be decisive when alternative mechanism sketches are pushed down to lower-level entities on which critical tests can then be performed.
Pearl's front-door criterion for the identification of a causal effect is a powerful and illuminating perspective on the explanatory power of mechanisms. It clearly shows that the identification of a causal effect via a mechanism requires that the mechanism be isolated and exhaustive and that its variables be observed. For such a mechanism to count as a sufficiently deep explanation, its causal pathways must be finely enough articulated that it meets whatever standard of bottoming out is maintained in the relevant field of study. If such a standard is not reached, then the causal effect is identified even though it is not accompanied by a sufficiently deep explanation. Instead, the identifying causal pathways represent a mechanism sketch that demands further analysis.
Considering this chapter and the strategies for causal effect estimation from prior chapters, we have come back full-circle to our initial presentation of causal modeling options in Chapter 1. We noted there, with reference to Figure 1.3, that a causal effect that is identified by both the back-door criterion and an instrumental variable is best explained when it is also identified by an isolated and exhaustive mechanism. This is the gold standard for an explanatory causal analysis, at least until a field decides that a crucial linkage within a mechanism must then be opened up and subjected to its own analysis.
In the next chapter, we turn in a different direction to consider the extent to which over-time data on an outcome variable can be used to identify and estimate a causal effect. One often hears presentations where scholars remark: I cannot get at causality because I do not have longitudinal data. We will argue in the next chapter that longitudinal data, although very helpful in many cases, are not the panacea that such statements seem to imply. Moreover, we will show that some long-standing techniques that are thought to reveal causal effects are strongly dependent on assumptions that are often entirely inappropriate and sometimes completely unrecognized.
1This position is equivalent to assuming that a more encompassing DAG exists that is applicable to the entire population and that the diagram in Figure