Assessing heterogeneity in a matching estimation of endogenous treatment effect

The traditional matching methods for the estimation of the treatment parameters are often affected by selectivity bias due to the endogenous joint influence of latent factors on the assignment to treatment and on the outcome. In this study, we show that the influence of unobserved factors involves a cross-correlation between the endogenous components of the propensity scores and causal effects. A correction for the effects of this correlation on matching results leads to a reduction of bias. We apply this correction in the estimation of the effect of retirement of man on the division of housework in the Italian couples, using the cross-sectional Time Use data provided by Istat. A sensitivity analysis is also provided to check the robustness of our findings.