Primary Submission Category: Matching, Weighting
Quantifying Practical Overlap in Causal Inference via KL Projections
Authors: Geondo Park, Juyeon Kim, Kwonsang Lee,
Presenting Author: Geondo Park*
Assessing overlap is an essential task in causal inference, as limited overlap undermines identifiability and leads to unstable estimators. In practice, overlap is most often evaluated through visual inspection of propensity score distributions. Although overlap is frequently discussed in connection with methods that improve estimation, such as trimming or overlap weighting, there is limited work on directly measuring how much overlap is present.
We propose a likelihood-based framework for quantifying practical overlap using Kullback-Leibler projections. The approach defines a common component as the distribution that best approximates the treated covariate distribution while remaining representable as a mixture component of the control population. This construction yields a smooth, distribution-level characterization of overlap that avoids explicit density estimation. An overlap parameter is defined as the largest fraction of the control population that can be retained while maintaining sufficient distributional proximity to the treated group. Simulations and empirical examples with known overlap challenges illustrate how the proposed measure provides a principled early-stage diagnostic prior to causal effect estimation.