Do Instrumental Variables Belong in Propensity Scores?
We find that, in the case of linear adjustment, using an instrumental variable as a predictor variable in a propensity score matching estimator yields greater inconsistency than would be obtained by ignoring selection. This additional inconsistency is increasing in the predictive power of the instrument. In the case of stratification, in the presence of a strong instrument, propensity score matching yields greater inconsistency than does the naive estimator and in the presence of a weak instrument, the two approaches produce equal inconsistency.
Our results are further illustrated with two empirical examples: one, the Tennessee STAR experiment, with a strong instrument and the other, the Swan-Ganz catheterization dataset of Connors et al. (1996), with a weak instrument.
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