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Suppose one is interested in estimating causal effects in the presence ofpotentially unmeasured confounding with the aid of a valid instrumentalvariable. This paper investigates the problem of making inferences about theaverage treatment effect when data are fused from two separate sources, one ofwhich contains information on the treatment and the other contains informationon the outcome, while values for the instrument and a vector of baselinecovariates are recorded in both. We provide a general set of sufficientconditions under which the average treatment effect is nonparametricallyidentified from the observed data law induced by data fusion, even when thedata are from two heterogeneous populations, and derive the efficiency boundfor estimating this causal parameter. For inference, we develop both parametricand semiparametric methods, including a multiply robust and locally efficientestimator that is consistent even under partial misspecification of theobserved data model. We illustrate the methods through simulations and anapplication on public housing projects.

On Semiparametric Instrumental Variable Estimation of Average Treatment Effects through Data Fusion