Propensity Score Matching without Conditional Independence Assumption - With an Application to the Gender Wage Gap in the United Kingdom

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Estimation of Quantile Treatment Effects with Stata (2010, methodology): “Frölich and Melly (2008) showed that ∆ for the compliers is identified under a somewhat weaker version of assumption 3, and they proposed the following estimator:”
The Finite Sample Performance of Inference Methods for Propensity Score Matching and Weighting Estimators (2018, methodology): “Inference in treatment effect estimation is frequently based on the (standard) nonparametric bootstrap (see Efron 1979 or Horowitz 2001, among others).”
Unconditional Quantile Treatment Effects Under Endogeneity (2007, unknown): “When the conditional distribution is estimated by local regression or by nearest neighbor regression, we obtain the estimator proposed, for example, in Frölich (2007b).”
Unemployed and their caseworkers: should they be friends or foes? (2010, unknown): “Frölich (2007) showed that mean independence (3) is nevertheless sufficient for consistency of propensity score matching.)”