Multiply robust two-sample instrumental variable estimation
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Although instrumental variable (IV) methods are widely used to estimate causal effects in the presence of unmeasured confounding, the IVs, exposure and outcome are often not measured in the same sample due to complex data harvesting procedures. Following the influential articles by Klevmarken (1982) and Angrist & Krueger (1992, 1995), numerous empirical researchers have applied two-sample IV methods to perform joint estimation based on an IV-exposure sample and an IV-outcome sample. This paper develops a general semi-parametric framework for two-sample data combination models from a missing data perspective, and characterizes the efficiency bound based on the full data model. In the context of the two-sample IV problem as a specific example, the framework offers insights on issues of efficiency and robustness of existing estimators. We propose new multiply robust locally efficient estimators of the causal effect of exposure on the outcome, and illustrate the methods through simulation and an econometric application on public housing projects.
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