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Old and New Instrumental Variables Models for Causal Inference: A Biostatistician's Futile Redevelopment?

Anirban Basu, University of Washington 
*Paul Rathouz, University of Wisconsin-Madison 
Joseph Terza, Indiana U Purdue U Indianapolis 

Keywords: instrumental variables, GMM, causal inference, endogeneity, confounding

In this work, I re-examine classical non-linear instrumental variables (IV) models with three main goals in mind: 1. To cast IV models in a counter-factual framework, 2. To consider general (versus binary) treatment variables, and 3. To develop identifying assumptions for IV models in terms of general conditional independence arguments (rather than in terms of uncorrelatedness or in terms of independence of residuals in specific models). In carrying out this program, I do the following: 1. Clarify the target of inference in IV estimation. 2. Derive ``minimal' confounders, which I believe are the same as Frangakis' ``principle strata'. 3. Group IV models and approaches into two main classes characterized by their inferential targets. One class fully involves fully specified models and can be estimated with 2SRI; the other is marginally specified and can be estimated with GMM. 4. Develop GMM estimators for this latter class of models.

This paper is a work in progress. I am very interested in feedback from workshop participants on the content and implications of this paper.