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8.1 applies only to the joint probability distribution for compliers
2Angrist and Krueger could deal with this problem by conditioning on a measure of work experience, but in their data no such variable is available. The only alternative with their data, which is common in the literature, is to attempt to untangle the effects by conditioning on age (which is typically done within an age-heterogeneous sample). However, this form of conditioning does not completely explain away the association between schooling and work experience, as is widely recognized (see Card 1999).
3The citations here are for a discussion of Samuel Stouffer's research in The American Soldier (which we also discuss in Chapter 1). Patricia Kendall was the lead author for this piece, and yet she is almost never cited in the derivative literature as a contributor to this language. Because it is often written that Lazarsfeld presented and discussed this basic typology in many places, it is possible that it is fair to credit him disproportionately for these ideas. Our reading of the literature, however, does not yield a clear interpretation. But, it does suggest to us that the Kendall has received less credit than she deserved.
4They also lay out a third form of elaboration, referred to as P-type elaboration (or specification). Here, the goal is to focus on the relative size of the partial relationship [between and within strata of the test factor ] in order to specify the circumstances under which the original relation is more or less pronounced (Kendall and Lazarsfeld 1950:157). This type of elaboration is appropriate when the test factor is related to either or but not both. We ignore this form of elaboration here, as we focus on variables that are related to both the causal and outcome variables.
5Note, further, that one can then assess the portion of the total variation in and that can be attributed to the pathway through . This calculation can be useful, but it does not identify the amount of the causal effect that is explained by . The problem is that the association between and that is not attributable to cannot be apportioned across the two unblocked paths and .
6A chapter from his book was also published in 2001 in the European Sociological Review as Causation, Statistics, and Sociology, which then received comments from a variety of scholars, including the statisticians David Cox and Nanny Wermuth (whose response we will discuss later). Our citations are to the 2001 piece.
7It is unclear from this passage what Goldthorpe means by in principle. However, on the next page of the article, he offers an example that reveals that his conception of a manipulation can be very narrow. Following an example of Holland (1986), he introduces mechanistic variables and argues that in so doing he has produced a causal narrative that has nothing to do with hypothetical manipulations/interventions and hence cannot be represented in a counterfactual framework. The argument seems to be that the mechanistic variables are non-manipulable because they are typically voluntary decisions of an individual. Woodward (2003) rejects such an anthropomorphic account of a manipulation/intervention.
8By our reading, Goldthorpe ends up back at the counterfactual model at this point. His defense against such a reading is: ... while it might seem that, at this stage, attention does after all come to focus on the effects of -- given -- causes rather than on the causes of effects, this is within the context not of randomized experimental design but of (what should be) a theoretically informed account of a generative process that is subject to ongoing evaluation (Goldthorpe 2000:13).
9It is unclear from the foregoing passage what the problematic other processes are meant to be. Clearly, they must come in two different forms: (1) other mechanisms that are completely independent of the postulated mechanism of primary interest (2) other mechanisms that interact with the postulated mechanism of primary interest. If one is estimating the effects of a cause, it is only the latter that are problematic for the evaluation of mechanisms, and hence for the evaluation of causal accounts based on mechanisms. See our earlier discussion of partial identification via the front-door criterion.
10But, we are somewhat more traditional in favoring mechanisms that are formal models, as we are less convinced of the utility of many simulation-based methods of theory construction (see Hedström 2005:76-87, 131-6, 149 on the appeal of such techniques). We agree with Humphreys' (2004:132) caution: Agent-based models are a powerful addition to the armory of social scientists, but as with any black-box computational procedures, the illusion of understanding is all to easy to generate.
11Hedström and Swedberg (1998) take a different reading of the literature that followed from the Lazarsfeldian tradition, focusing critical attention on the work of Duncan and his colleagues (see their quotation on page 9). Then, in his 2005 book, Hedström criticized Duncan's models of socioeconomic status (see pages 102-3). As is clear in our main text, our reading of Duncan's record on this issue is somewhat less negative, although we noted in Chapter 1 that it is hard to pin down exactly what Duncan recommended in the theory and the practice of causal modeling. Hedström's negative opinion, however, is certainly applicable to much scholarship that followed Duncan's lead, a position that we suspect Duncan too would have agreed with and which we note in Chapter 1.
Goldthorpe (2001) also has a different reading of Lazarsfeld's method of elaboration. He argues that the robust dependence tradition of causal analysis, which he regards as exemplified by Lazarsfeld's work, was based almost entirely on the search for prior causes that can explain away correlations (see Goldthorpe 2001:2-3). This seems inconsistent with what Kendall and Lazarsfeld (1950) refer to as interpretation, as we noted earlier.
12We do not attempt to give a full summary of the fall of covering law models, since many accessible texts exist in philosophy (see citations in the main text) and others that are written for social scientists alone (e.g., Gorski 2004 and Hedström 2005). Nor do we give a full explication of the variety of positions that have replaced the covering law model, as these too are well summarized elsewhere (see citations in the main text for realist models in particular, as well as the variety of naturalist positions that contend with them).
13Given Bunge's position, one then necessarily wonders: How does one discover these crucial explanatory mechanisms? Bunge's (2004:200) guidance is: There is no method, let alone logic, for conjecturing mechanisms. True, Peirce wrote about the method of abduction, but `abduction' is synonymous with `conjecturing', and this -- as Peirce himself warned -- is an art, not a technique. One reason is that, typically, mechanisms are unobservable, and therefore their description is bound to contain concepts that do not occur in empirical data.
14As best we can tell, Woodward (2003; Section 4.6) takes this position, noting the need for only a rather limited backing relationship between causal claims and laws.
15Methodological individualism is the basic position of Goldthorpe (2000) and Hedström (2005), as influenced heavily by the scholarship of Raymond Boudon (see Boudon 1998 and citations therein).
16Gorski (2004) endorses the causal process model of Wesley Salmon, as developed in Salmon's work from the 1970s and early 1980s (see Salmon 1984). Given the ways in which Salmon's work has developed since then, turning completely toward causal mechanical ideas based on the notion of conserved quantities, his ideas now seem completely at odds with Gorski's statement that Social science is nothing but history. The real error was ever to think it could be anything more (Gorski 2004:30).
17 In fact, the first author found it convincing and inspiring when writing Morgan (2005).
18See also the discussion of modularity in Woodward (2003, Ch. 7).
19A critical realist could escape from this position in a variety of ways: asserting irreducibility and transcendentalism and then, more specifically, by arguing in the end that the data that one is forced to consider are but a poor reflection of the phenomena that the mechanism truly does explain. For all of these reasons, the lack of observed explanatory power for observed events would then be argued to be untroubling. This position, however, then becomes a variant of an appeal to a hidden but presupposed valid underlying structure, which Woodward convincingly argues cannot be an acceptable explanatory strategy for any field that hopes to resolve its explanatory controversies because ... the appeal to hidden structure makes it too easy to protect one's favored theory of explanation from genuine counterexamples (Woodward 2003:175). Moreover, if the particularities in the data are merely a poor reflection of the phenomenon that the mechanism is supposed to explain, then presumably whatever generates the mismatch can be encoded in the mechanism that explains both the genuine phenomenon of interest and the process that generates the misleading data.