The Propensity Score: A Means to An End

Propensity score matching is a prominent strategy to reduce imbalance in observational studies. However, if imbalance is considerable and the control reservoir is small, either one has to match one control to several treated units or, alternatively, discard many treated persons. The first strategy tends to increase standard errors of the estimated treatment effects while the second might produce a matched sample that is not anymore representative of the original one. As an alternative approach, this paper argues to carefully reconsider the selection equation upon which the propensity score estimates are based. Often, all available variables that rule the selection process are included into the selection equation. Yet, it would suffice to concentrate on only those exhibiting a large impact on the outcome under scrutiny, as well. This would introduce more stochastic noise making treatment and comparison group more similar. We assess the advantages and disadvantages of the latter approach in a simulation study.