Causality, Confounding, and Control

In a previous paper, Russo et al. (2006), causality is considered in the framework of structural models, i.e. statistical models characterized by parameters that are stable over a large class of interventions or of environmental changes and that take into account background and contextual knowledge. From this statistical viewpoint, causality is defined in terms of exogeneity in a structural model. This approach allows us to attain a concept of causality that is internal or relative to the structural model itself. Thus our knowledge of causal relations depends on structural models that mediate epistemic access to causal relations. In the social sciences, structural models correspond to causal structures that are much more complex than simple causal relations such as X causes Y . Russo et al. (2006) mentions some practical difficulties such as covariate sufficiency, no confounding, etc. without developing a systematic analysis of those issues. In the present paper we examine more thoroughly the concept of exogeneity and the problem of confounding and control. More specifically, we show that confounding due to latent variables raises substantial problems for exogeneity. We start by examining the issue of exogeneity in a conditional structural model and then proceed with the concept of confounding and its impact on causal modelling. We conclude the paper with a brief discussion on how and when to control for confounding. Exogeneity has a long history in the foundations of statistical modelling. In econometrics, Hood and Koopmans (1953) gathers a number of pionneering contributions from the Cowles Foundation, Engle et al. (1983) and Florens and Mouchart (1985), among others, elaborate further these con-