Bayesian model averaging for propensity score matching in tax rebate

Propensity Score Matching is a popular approach to evaluate treatment effects in observational studies. However, when building the underlying propensity score model practitioners often overlook the issue of model uncertainty and its consequences. We tackle this problem by Bayesian Model Averaging (BMA) with an application to the 2014 Italian tax credit reform (the so-called Renzi bonus). Model uncertainty has a great impact on the estimated treatment effects. BMA-based estimates point towards a significant effect of the rebate on food consumption only for liquidity constrained house- holds; conversely, model selection procedures sometimes produce results incompatible with the consumption smoothing hypothesis.