The Analysis of Over-determined Outcomes: Identification in the Presence of Functional Dependence.

A variety of different literatures have examined the problem of identifying and estimating the effects of different independent variables when an outcome is over-determined. This problem has been most extensively analyzed in the context of the Age-Period-Cohort (APC) model, though it has been an important concern in the evaluation research literature, and in comparative-historical analysis. All three literatures have, broadly speaking, offered the same generic solution. In particular, they have suggested that estimation may be possible if one specifies the mechanisms by which each independent variable affects the outcome. Formally, this is equivalent to specifying the functional form of the relationship between each independent variable and the dependent variable in such a way, that the independent variables are no longer linear dependent. The above literatures have only offered a limited, if any, formal justification for this solution. This paper provides a formal analysis of the problem of identifying the separate causal effects of different variables in the presence of an over-determined outcome. Building on Pearl's front-door criteria for the identification of causal effects, we provide a formal theory of identification for over-determined outcomes. This theory provides a formal justification for the earlier approach and demonstrates the assumptions behind it. In addition, the theory shows that a broader set of identification strategies are available and that under certain circumstances, a model specification test is possible. We end the paper by arguing that Pearl's front-door criteria provides the basis for a general approach to the analysis of over-determined outcomes across a wide variety contexts. We demonstrate the useful this approach by analyzing an empirical example. [ABSTRACT FROM AUTHOR]