  It has been argued that innovation in transaction technology may modify the
cash holding behaviour of agents, as debit card holders may either withdraw
cash from ATMs or purchase items using POS devices at retailers. In this paper,
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 (SHIW). 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.
