  Over the past ten years, propensity score methods have made an important
contribution to improving generalizations from studies that do not select
samples randomly from a population of inference. However, these methods require
assumptions and recent work has considered the role of bounding approaches that
provide a range of treatment impact estimates that are consistent with the
observable data. An important limitation to bound estimates is that they can be
uninformatively wide. This has motivated research on the use of propensity
score stratification to narrow bounds. This article assesses the role of
distributional overlap in propensity scores on the effectiveness of
stratification to tighten bounds. Using the results of two simulation studies
and two case studies, I evaluate the relationship between distributional
overlap and precision gain and discuss the implications when propensity score
stratification is used as a method to improve precision in the bounding
framework.
