Misspecification and the Propensity Score: When to Leave Out Relevant Pre-Treatment Variables
Clarke, Kevin A.
The popularity of propensity score matching has given rise to a robust, albeit informal, debate concerning the number of pre-treatment variables that should be included in the propensity score. The standard practice is to include all available pre-treatment variables in the propensity score. We demonstrate that this approach is not always optimal for the goal of reducing bias in the estimation of a treatment effect. We characterize conditions under which including an additional relevant variable in a propensity score increases the bias on the effect of interest across a variety of different implementations of the propensity score methodology. We find that matching within propensity score calipers is slightly more robust against such bias than other common methods.
omitted variable bias
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