Do debit cards decrease cash demand?: causal inference and sensitivity analysis using principal stratification.

It has been argued that the use of debit cards may modify the cash holding behaviour, as debit card holders may either withdraw cash from automated teller machine or purchase items using point-of-sale devices at retailers. Within the Rubin causal model, we investigate the causal effects of the use of debit cards on the cash inventories held by households using data from the Italy Survey of Household Income and Wealth. We adopt the principal stratification approach to incorporate the share of debit card holders who do not use this payment instrument. We use a regression model with the propensity score as the single predictor to adjust for the imbalance in observed covariates. We further develop a sensitivity analysis approach to assess the sensitivity of the proposed model to violation to the key unconfoundedness assumption. Our empirical results suggest statistically significant negative effects of debit cards on the household cash level in Italy.