PSM is a non-parametric analysis of measuring impact. It does not require distributional assumptions. However, the observed covariates entering the probit or logit models for the propensity score would have to satisfy the conditional independence assumption (CIA) assumptions. How do you ensure CIA holds when you choose characteristics in probit/logit models to estimate propensity scores? Do you use any formal test?
Yep! You must be sure the statistical tests support the CIA as an econometric pre-requisite. The tests are similar to the exogeneity tests in the literature.
Hi Shaheen,
Technically there is no way to ensure that CIA holds, it is an assumption. In matching (propensity score, covariate or otherwise) the assumption that potential outcomes are independent of treatment status (CIA) is best defended using the following arguments: (1) that the covariates you choose jointly determine (fully) the selection process and outcomes, (2) there are no unobserved confounders, or that the logical unobserved confounders are highly correlated with the covariates in your model, and (3) you have a high degree of post-match balance across your covariates. The first two are untestable arguments that you must defend in the description of your research. The third is one of the most important aspects of a matching-based estimation strategy. Matching is a quasi-experimental approach which attempts to replicate experimental conditions be ensuring that all determinants of outcomes (other than treatment status) are similar between the treated group and their matched controls. Thus, post-match balance tests provide information on how well matching has "replicated" the experimental benchmark. But keep in mind, even if perfect balance is achieved, CIA is still an assumption.
Best,
Merlin
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