Ecological Regression with Partial Identification
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We study a partially identified linear contextual effects model for ecological inference, and we describe how to perform inference on the district level parameter averaging over many precincts in the presence of the non-identified parameter of the contextual effect. We derive various bounds for this non-identified parameter of the contextual effect, from the tightest possible, to ones that may be more practical for applications. This may be regarded as a first attempt to limit the scope of non-identifiability in linear contextual effects models. As an application, the linear contextual model implies a "regression bound" for the district level parameter of interest, which can be intersected with the model-free bound of Duncan and Davis (1953) to obtain a shorter width than using the model-free bounds alone, at varying confidence levels.
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