> 6. Slogan: "causal net before functional model". As described in Spirtes, Glymour and Scheines (1993,2001) and Pearl (2000), these formalisms are equivalent for the purposes of determining the population distributions resulting from the implementation of policies,.
A little more discussion follows: It is true that traditionally functional relationships (e.g. linearity) have been assumed in structural equation models, but more modern approaches are non-parametric, in which case, at a conceptual level, there is no difference between the two. [As a side note: Structural equation models can be interpreted as relating to individual causal effects - i.e. inferring causes from effects, "Would John have a headache had he not drunk coffee this morning given that he did drink coffee and does have a headache", but this has not been done by econometricians - whereas this is not true of "causal nets". However, such inferences are based on assumptions that cannot in general be tested even in experimental contexts. Further Econometricians have typically not drawn such inferences from their models, hence this is not directly relevant here. See Pearl (2000) Ch.5 and 7 for further discussion.) > 4. Consequently it would be better to use causal Bayesian networks instead, > since in that case we only need to estimate the probability distribution of > each variable conditional on its direct causes. Such models should be > checked (one should check that the causal Markov condition holds for the > model and that the model is robust for forcasting and modeling > interventions) and refined as necessary. If "only" we ever knew the direct causes and could directly check the Markov property! However, such conditional independence assumptions are equivalent to the assumptions made by the coresponding structural equation model. Note that in general there will be more than one "causal net" obeying a given set of conditional independence relations, hence the fact that our data are compatible with the independence relations given by a given causal model does not verify the model, to the extent that the data confirms or supports the proposed model, it also supports every other model in the given Markov equivalence class. Even this inference requires the (untestable) assumption that conditional independence relations present in the population distribution only arise through causal structure and not through cancellation of parameters (so-called violations of faithfulness or stability). In general it is often unclear whether all of the relevant variables have been included, which means that models with hidden variables (or "correlated errors" or "semi-Markovian") must also be considered, thereby expanding further the class of causal models that are not ruled out by the data. This problem is equally present for both formalisms. (Again see the above references for more discussion.) In general, on finite samples, it is often unrealistic to hope to reliably determine the conditional independence structure holding in the population non-parametrically. For this reason functional forms are often assumed (e.g. "noisy-or" in the causal net literature; linearity in Econometrics). Such problems have been particularly acute in Econometrics where datasets have traditionally been rather small (this is starting to change). To summarize, there is no significant distinction between the two approaches. The primary practical problems present in applications of structural equation models - lack of data, large numbers of possible variables and possible models, are also present for causal nets. It is true that users of structural equation models have often been unclear or even unaware of the causal interpretation of their models and this has led to much confusion and obscurity. In this regard, the community of causal net modellers may have some advantage (though this issue is also often not addressed in many Bayes Net applications). The issues of stationarity raised by Peter McBurney are of course also of concern in many Econometric applications. Feedback is another possibility in many econometric settings For more discussion of this see Lauritzen and Richardson "Chain graph models and their causal interpretations (with discussion)", (2001) Journal of the Royal Statistical Society Series B. Thomas Richardson Department of Statistics University of Washington
