  Motivated by recent findings in the field of consumer science, this paper
evaluates the causal effect of debit cards on household consumption using
population-based data from the Italy Survey on Household Income and Wealth
(SHIW). Within the Rubin Causal Model, we focus on the estimand of population
average treatment effect for the treated (PATT). We consider three existing
estimators, based on regression, mixed matching and regression, propensity
score weighting, and propose a new doubly-robust estimator. Semiparametric
specification based on power series for the potential outcomes and the
propensity score is adopted. Cross-validation is used to select the order of
the power series. We conduct a simulation study to compare the performance of
the estimators. The key assumptions, overlap and unconfoundedness, are
systematically assessed and validated in the application. Our empirical results
suggest statistically significant positive effects of debit cards on the
monthly household spending in Italy.
