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Abstract:
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In this talk we consider causal models containing an instrumental variable (Z), a treatment (X) and a response (Y) in which Z, X and Y are categorical. We assume that Z is randomized and that Z has no direct effect on the outcome Y. We first consider the problem of characterizing those distributions over potential outcomes that are compatible with a given observed distribution P(X,Y | Z). We also consider restrictions imposed on the observed distribution by the instrumental variable model. We will show how these restrictions may be used to test the assumptions present in the model. In addition our characterization of the model for the observables leads to 'transparent' parametrizations under which identified and non-identified parameters are clearly distinguished.
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